A022583 Expansion of Product_{m>=1} (1+x^m)^18.

1, 18, 171, 1158, 6309, 29430, 121962, 460008, 1605996, 5254334, 16260867, 47949804, 135509922, 368764290, 970099191, 2475106170, 6141671649, 14856839874, 35107961175, 81189855828, 184033842021, 409446105486, 895231350108, 1925717858910, 4079428991751, 8518121246538

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=18 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^18: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)^18,{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)^18)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (3/2)^(1/4) * exp(Pi * sqrt(6*n)) / (1024 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (18/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017