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

Author

Shalosh B. Ekhad, May 03 2012

Keywords

• sign
• more

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

Examples

			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.
		

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, 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.

Programs

Maple

See above link to HANS (maple package).

Formula

See above article for an efficient recurrence.