A022576 Expansion of Product_{m>=1} (1+x^m)^11.

1, 11, 66, 297, 1122, 3740, 11341, 31922, 84535, 212707, 512369, 1188353, 2666048, 5807296, 12319659, 25518757, 51725289, 102786959, 200568907, 384847199, 727019260, 1353654049, 2486522369, 4509972819, 8083287432, 14326409152, 25124415635, 43622744968, 75026666913, 127882738709

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=11 of A286335.

Cf. A000009.

Programs

Magma

Coefficients(&*[(1+x^m)^11:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^11,{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)^11)) \\ G. C. Greubel, Feb 26 2018

Formula

a(n) ~ (11/3)^(1/4) * exp(Pi * sqrt(11*n/3)) / (128 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (11/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017