A022587 Expansion of Product_{m>=1} (1 + x^m)^22.

1, 22, 253, 2046, 13134, 71368, 341275, 1473494, 5848810, 21628002, 75261384, 248403586, 782547909, 2365168542, 6887441198, 19393122562, 52959869787, 140631776582, 363943223941, 919706094494, 2273411319069, 5505315501136, 13078268135683, 30514651732686, 70005101272876

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=22 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^22: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)^22,{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)^22)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (11/6)^(1/4) * exp(Pi * sqrt(22*n/3)) / (4096 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (22/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017