A022596 Expansion of Product_{m>=1} (1+q^m)^32.

1, 32, 528, 6016, 53384, 393920, 2517824, 14329600, 74059812, 352722720, 1565583648, 6533812352, 25823152256, 97218393280, 350348856704, 1213526698240, 4054279504266, 13103911398400, 41081428394096, 125210147216000, 371754750363712, 1077136199182976, 3050503922469440

Offset

0,2

Comments

In general, for k > 0, if g.f. = product_{m>=1} (1+q^m)^k, then a(n) ~ k^(1/4) * exp(Pi * sqrt(k*n/3)) / (2^((k+3)/2) * 3^(1/4) * n^(3/4)) * (1 + (Pi*k^(3/2) / (48*sqrt(3)) - 3^(3/2) / (8*Pi*sqrt(k))) / sqrt(n)). - Vaclav Kotesovec, Mar 05 2015, extended Jan 16 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ exp(Pi * 4 * sqrt(2*n/3)) / (65536 * 6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^32, {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)^32)) \\ G. C. Greubel, Mar 20 2018
(Magma) Coefficients(&*[(1+x^m)^32:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Mar 20 2018

Crossrefs

Column k=32 of A286335.

Sequence in context: A162379 A162739 A010984 * A130609 A154306 A004417

Adjacent sequences: A022593 A022594 A022595 * A022597 A022598 A022599

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved