A022586 Expansion of Product_{m>=1} (1+x^m)^21.

1, 21, 231, 1792, 11067, 58002, 268093, 1120899, 4315269, 15497986, 52441347, 168487473, 517184185, 1524390777, 4332440454, 11914441196, 31798680774, 82574231187, 209091601271, 517272712845, 1252351944165, 2971700764941, 6920411525727, 15835150526244, 35640093688017

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=21 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^21: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)^21,{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)^21)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ 7^(1/4) * exp(Pi * sqrt(7*n)) / (4096 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (21/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017