Question: What Japanese anime series is inspired by a fairy tale written by Hans Christian Andersen?

Context paragraphs:
Allumette: A Fable: Allumette; A Fable, with Due Respect to Hans Christian Andersen, the Grimm Brothers, and the Honorable Ambrose Bierce, by Tomi Ungerer, was originally published in 1974.  It is a "reimagining" of "The Little Match Girl" by Hans Christian Andersen.  The book's extended title references Andersen, for "The Little Match Girl", as well as fairy tale authors the Brothers Grimm, and satirist Ambrose Bierce.  The book was initially published in 1974, and carried in the United States by Parents' Magazine Press and Scholastic, both bargain retailers.  It was also briefly reprinted in 1986, but has since gone out of print again.

The Ugly Duckling: "The Ugly Duckling" (Danish: "Den grimme ælling") is a literary fairy tale by Danish poet and author Hans Christian Andersen (1805–1875).  The story tells of a homely little bird born in a barnyard who suffers abuse from the others around him until, much to his delight (and to the surprise of others), he matures into a beautiful swan, the most beautiful bird of all.  The story is beloved around the world as a tale about personal transformation for the better.  “The Ugly Duckling” was first published 11 November 1843, with three other tales by Andersen in Copenhagen, Denmark to great critical acclaim.  The tale has been adapted to various media including opera, musical, and animated film.  The tale is completely Andersen's invention and owes no debt to fairy tales or folklore.

New Fairy Tales (1844): New Fairy Tales (Danish: "Nye Eventyr" ) is a collection of four fairy tales written by Hans Christian Andersen and published by C. A. Reitzel in Copenhagen, Denmark on 10 November 1843.  As was customary at the time however, the title page is dated 1844.  The tales are completely Andersen's invention, owe no debt to folk or fairy lore, and are the most autobiographical of his several fairy tale collections.  The collection was received enthusiastically by the Danish critics and public and became Andersen's break-through in the fairy tale genre.  "The Nightingale" and "The Ugly Duckling" have been adapted to various forms of drama.

The Snow Queen: "The Snow Queen" (Danish: "Snedronningen" ) is an original fairy tale written by Danish author Hans Christian Andersen.  The tale was first published 21 December 1844 in "New Fairy Tales.  First Volume.  Second Collection.  1845."  (Danish: "Nye Eventyr.  Første Bind.  Anden Samling.  1845." )  The story centres on the struggle between good and evil as experienced by Gerda and her friend, Kai.

The Nightingale (fairy tale): "The Nightingale" (Danish: "Nattergalen") is a literary fairy tale written by Danish author Hans Christian Andersen about an emperor who prefers the tinkling of a bejeweled mechanical bird to the song of a real nightingale.  When the Emperor is near death, the nightingale's song restores his health.  Well received upon its publication in Copenhagen in 1843 in "New Fairy Tales", the tale is believed to have been inspired by the author's unrequited love for opera singer Jenny Lind, the "Swedish nightingale".  The story has been adapted to opera, ballet, musical play, television drama and animated film.

Princess Tutu: Princess Tutu (Japanese: プリンセスチュチュ , Hepburn: Purinsesu Chuchu ) is a Japanese magical girl anime series created by Ikuko Itoh in 2002 for animation studio Hal Film Maker.  Inspired by ballet and fairy tales, particularly "The Ugly Duckling" and "Swan Lake", the story follows a duck who is transformed into the mythical ballerina Princess Tutu in order to save the shattered heart of a storybook prince come to life.

Hans Christian Andersen Museum: The Hans Christian Andersen Museum is a museum dedicated to famous author Hans Christian Andersen in Odense, Denmark.  It is located in the building which is thought his birthplace, a small yellow house on the corner of Hans Jensens Stræde and Bangs Boder in the old town.  In 1908, the house was opened as the Hans Christian Andersen Museum.  It documents his life from his childhood years as the son of a struggling shoemaker, to his schooling, career as an author, and later life, with artefacts providing an insight into his acquaintances and adventures.  Andersen's childhood home is on Munkemøllestræde not far from the cathedral.  He lived in the little half-timbered house from the age of two until he was 14.  Opened as a museum in 1930, the house contains an exhibition of the cobbling tools used by his father and other items based on Andersen's own descriptions.

Thumbelina: "Thumbelina" (Danish: "Tommelise" ) is a literary fairy tale written by Danish author Hans Christian Andersen first published by C. A. Reitzel on 16 December 1835 in Copenhagen, Denmark, with "The Naughty Boy" and "The Traveling Companion" in the second installment of "Fairy Tales Told for Children."  "Thumbelina" is about a tiny girl and her adventures with appearance- and marriage-minded toads, moles, and cockchafers.  She successfully avoids their intentions before falling in love with a flower-fairy prince just her size.

Thumbelina: A Magical Story: Thumbelina: A Magical Story (おやゆび姫物語 , Oyayubi Hime Monogatari , lit.  "The Story of Princess Thumbelina") is a Japanese anime series produced by Enoki Films and adapted from the original Hans Christian Andersen fairy tale "Thumbelina" by Akiyoshi Sakai.  It premiered in Japan on TV Tokyo on September 30, 1992 and ran for twenty-six episodes until its conclusion on March 31, 1993.

Andersen Monogatari (TV series): Hans Christian Andersen Stories (アンデルセン物語 , Anderusen Monogatari ) is a Japanese anime series by Mushi Productions and aired on Fuji TV from January 3 to December 26, 1971.  It's about the legendary stories of Hans Christian Andersen.

Supporting paragraphs: Princess Tutu The Ugly Duckling
Answer: Princess Tutu