A022595 Expansion of Product_{m >=1} (1+q^m)^31.

1, 31, 496, 5487, 47337, 340039, 2118385, 11763911, 59384158, 276491170, 1200703594, 4906332242, 18998567031, 70120824201, 247873586247, 842625902072, 2764160465375, 8776228494225, 27038961793349, 81019542614568, 236575764828149, 674366427736330, 1879524499776454

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ (31/3)^(1/4) * exp(Pi * sqrt(31*n/3)) / (131072 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^31, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)

Prog

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+q^n)^31)) \\ G. C. Greubel, Mar 20 2018
(Magma) Coefficients(&*[(1+x^m)^31:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Mar 20 2018

Crossrefs

Column k=31 of A286335.

Sequence in context: A162378 A162737 A010983 * A125488 A319427 A241888

Adjacent sequences: A022592 A022593 A022594 * A022596 A022597 A022598

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(19) onward added by G. C. Greubel, Mar 20 2018

Status

approved