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, -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

Table of n, a(n) for n=1..8.

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, Rademacher's Infinite Partial Fraction Conjecture is (almost certainly) False, Oct 21 2011; Local copy, pdf file only, no active links.

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

Adjacent sequences: A182520 A182521 A182522 * A182524 A182525 A182526

Keyword

sign,more

Author

Shalosh B. Ekhad, May 03 2012

Status

approved