A022580 Expansion of Product_{m>=1} (1+x^m)^15.

1, 15, 120, 695, 3285, 13443, 49305, 165795, 519240, 1531960, 4295046, 11520000, 29718605, 74060355, 178930605, 420368858, 962785560, 2154411120, 4718952965, 10134292275, 21369644184, 44300604895, 90390209685, 181706747280, 360207189225, 704726281002, 1361748557400

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=15 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^15: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)^15,{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)^15)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ 5^(1/4) * exp(Pi * sqrt(5*n)) / (512 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (15/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017