A022578 Expansion of Product_{m>=1} (1+x^m)^13.

1, 13, 91, 468, 1989, 7384, 24739, 76427, 220948, 604175, 1575392, 3941847, 9511944, 22226049, 50458447, 111609537, 241099027, 509680951, 1056262792, 2149214288, 4299359012, 8465605408, 16424772637, 31429372312, 59365381608, 110770031489, 204315725953, 372772306309, 673125106316

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=13 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^13: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)^13,{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)^13)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (13/3)^(1/4) * exp(Pi * sqrt(13*n/3)) / (256 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (13/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017

Extensions

More terms added by G. C. Greubel, Feb 25 2018