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A182523
Rademacher's sequence C_{011}(N) times (2n)!, where C_{011}(N) is the coefficient of 1/(q-1) in the partial fraction decomposition of 1/((1-q)(1-q^2)...(1-q^N)).
2
-2, -6, -170, -9520, -874902, -118950678, -22370367448, -5550123527520
OFFSET
1,1
COMMENTS
Hans Rademacher conjectured that C_{011}(N) converge to -0.292927573960. This conjecture is false.
Named after the German-American mathematician Hans Adolph Rademacher (1892-1969). - Amiram Eldar, Jun 22 2021
REFERENCES
Hans Rademacher, Topics in Analytic Number Theory, Springer, 1973, p. 302.
LINKS
Andrew V. Sills and Doron Zeilberger, Rademacher's infinite partial fraction conjecture is (almost certainly) false, arXiv:1110.4932v1 [math.NT], 2011.
Andrew V. Sills and Doron Zeilberger, HANS (maple package); Local copy.
FORMULA
See above article for an efficient recurrence.
EXAMPLE
For n=1, the coefficient of 1/(q-1) in the partial fraction decomposition of 1/(1-q) is -1, multiplied by 2! this gives -2.
MAPLE
See above link to HANS (maple package).
CROSSREFS
Sequence in context: A199482 A168649 A135937 * A137532 A072116 A203430
KEYWORD
sign,more
AUTHOR
Shalosh B. Ekhad, May 03 2012
STATUS
approved