A022575 Expansion of Product_{m>=1} (1+x^m)^10.

1, 10, 55, 230, 815, 2562, 7360, 19700, 49755, 119700, 276278, 615130, 1326965, 2783360, 5693305, 11384326, 22299655, 42865280, 80983060, 150571340, 275840009, 498410280, 889056835, 1566896280, 2730474975, 4707724814, 8035618655, 13586253440, 22765030080, 37820087380

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=10 of A286335.

Cf. A000009.

Programs

Magma

Coefficients(&*[(1+x^m)^10: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)^10,{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)^10)) \\ G. C. Greubel, Feb 26 2018

Formula

a(n) ~ (5/6)^(1/4) * exp(Pi * sqrt(10*n/3)) / (64 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017