A022585 Expansion of Product_{m>=1} (1+x^m)^20.

1, 20, 210, 1560, 9255, 46724, 208510, 843320, 3145855, 10963160, 36042250, 112633760, 336622160, 966897820, 2680139300, 7193849624, 18752326235, 47590579080, 117840608100, 285228791880, 675978772326, 1570897356960, 3584273539170, 8038904002760, 17741382028085, 38563932406500

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=20 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^20: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)^20,{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)^20)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (5/3)^(1/4) * exp(2 * Pi * sqrt(5*n/3)) / (2048 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (20/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017