A022588 Expansion of Product_{m>=1} (1 + x^m)^23.

1, 23, 276, 2323, 15479, 87101, 430445, 1917349, 7839849, 29824583, 106646308, 361327079, 1167406906, 3615602714, 10780913004, 31061653709, 86741652761, 235404301651, 622271232287, 1605432041576, 4049617772390, 10002785010369, 24227747380447, 57613905606273, 134662398395411

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=23 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^23: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)^23,{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)^23)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (23/3)^(1/4) * exp(Pi * sqrt(23*n/3)) / (8192 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (23/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017