Question: When was the Kurt Vonnegut novel that appeared as lyrics in a song on the album Ambrosia first published?

Context paragraphs:
Asa Breed: Asa Breed is the third studio album by Matthew Dear.  It was released via Ghostly International in 2007.  The title comes from a character in the Kurt Vonnegut novel, "Cat's Cradle".

Venus on the Half-Shell: Venus on the Half-Shell is a science fiction novel by American writer Philip José Farmer, writing pseudonymously as "Kilgore Trout", a fictional recurring character in many of the novels of Kurt Vonnegut.  This book first appeared as a lengthy fictitious "excerpt"—written by Vonnegut, but attributed to Trout—in Vonnegut's "God Bless You, Mr. Rosewater" (1965).  With Vonnegut's permission, Farmer expanded the fragment into an entire standalone novel (including, as an in-joke, a scene that incorporates all of Vonnegut's original text).  Farmer's story was first published in two parts beginning in the December 1974 issue of "The Magazine of Fantasy and Science Fiction".  The plot, in which Earth is destroyed by cosmic bureaucrats doing routine maintenance and the sole human survivor goes on a quest to find the "Definitive Answer to the Ultimate Question," was paid homage by the later "Hitchhiker's Guide to the Galaxy" series.

While Mortals Sleep (short story collection): While Mortals Sleep is a collection of sixteen previously unpublished short stories by Kurt Vonnegut, released on January 25, 2011.  It is the third posthumously published Kurt Vonnegut book, the first being "Armageddon in Retrospect", the second being "Look at the Birdie".  The book begins with a foreword by Dave Eggers.  Illustrations by Vonnegut himself appear throughout.

Kurt Vonnegut's God Bless You, Mr. Rosewater: Kurt Vonnegut's God Bless You, Mr. Rosewater is a 1979 musical that marked the first collaboration of composer Alan Menken and writer Howard Ashman.  Based on Kurt Vonnegut's 1965 novel of the same name, the musical tells the story of Eliot Rosewater, a millionaire who develops a social conscience and creates a foundation to improve the lives of the citizens of an impoverished Indiana town.

Cat's Cradle: Cat's Cradle is the fourth novel by American writer Kurt Vonnegut, first published in 1963.  It explores issues of science, technology, and religion, satirizing the arms race and many other targets along the way.  After turning down his original thesis in 1947, the University of Chicago awarded Vonnegut his master's degree in anthropology in 1971 for "Cat's Cradle".

Ambrosia (album): Ambrosia is the self-titled debut album by Ambrosia.  It was released in 1975 on 20th Century Fox Records.  It spawned the top 20 chart single "Holdin' on to Yesterday" as well as the minor hit "Nice, Nice, Very Nice".  The latter sets to music the lyrics to a poem in Kurt Vonnegut's "Cat's Cradle".  The album was nominated for a Grammy Award for Best Engineered Recording (other than Classical).  Alan Parsons was the engineer for Ambrosia's first album and the producer for their second.

Galápagos (novel): Galápagos is the eleventh novel written by American author Kurt Vonnegut.  The novel questions the merit of the human brain from an evolutionary perspective.  The title is both a reference to the islands on which part of the story plays out, and a tribute to Charles Darwin on whose theory Vonnegut relies to reach his own conclusions.  It was first published in 1985 by Delacorte Press.

Tomorrow and Tomorrow and Tomorrow (short story): "Tomorrow and Tomorrow and Tomorrow" is a short story by Kurt Vonnegut originally written in 1953.  It was first published in "Galaxy Science Fiction" magazine in January 1954, where the story was titled "The Big Trip Up Yonder", which is the protagonist's euphemism for dying.  A revised version bearing the title "Tomorrow and Tomorrow and Tomorrow" appeared in Vonnegut's collection of short stories, "Canary in a Cat House" (1961), and was reprinted in "Welcome to the Monkey House" (1968).  The new title comes from the famous line in Shakespeare's play "Macbeth" starting "Tomorrow and tomorrow and tomorrow".

Jailbird: Jailbird is a novel by Kurt Vonnegut, originally published in 1979; it is regarded as Kurt Vonnegut's "Watergate novel."  The plot involves elements that include the U.S. labor movement of the late 19th and early 20th centuries, the dialectical back-and-forth of labor and management, Marxism and capitalism in the 1930s and 1940s, even up to the imperiousness of the Nixon administration.  "Jailbird" revolves around Walter F. Starbuck, a man recently released from a minimum-security prison in Georgia after serving time for his comically small role in the Watergate Scandal.  "Jailbird" is written as a standard memoir, revealing Starbuck's present situation, then coming full circle to tell the story of his first two days after being released from prison.

Look at the Birdie: Look at the Birdie is a collection of fourteen previously unpublished short stories by Kurt Vonnegut, released on October 20, 2009.  It is the second posthumously published Kurt Vonnegut book, the first being "Armageddon in Retrospect".

Supporting paragraphs: Ambrosia (album) Cat's Cradle
Answer: 1963