A022589 Expansion of Product_{m>=1} (1 + q^m)^25.

1, 25, 325, 2950, 21100, 126905, 667850, 3157725, 13667175, 54900675, 206841715, 736953800, 2499500175, 8113694575, 25320834800, 76253908740, 222308896150, 629146702350, 1732518057650, 4651937973250, 12201443983695, 31311905220800, 78732034002275, 194220161393825

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=25 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^25:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 25 2018

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^25,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^25)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ sqrt(5) * exp(5 * Pi * sqrt(n/3)) / (16384 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

Extensions

Terms a(20) onward added by G. C. Greubel, Feb 25 2018