A022572 Expansion of Product_{m>=1} (1+x^m)^7.

1, 7, 28, 91, 259, 665, 1589, 3585, 7707, 15925, 31808, 61677, 116536, 215180, 389194, 690935, 1206016, 2072700, 3511851, 5872545, 9701097, 15844866, 25606840, 40974528, 64956836, 102076289, 159084401, 245995792, 377574402, 575459136, 871189669, 1310492547, 1959326215, 2912370944

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A000009.

Column k=7 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^7: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)^7,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)

PARI

x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^7)) \\ Indranil Ghosh, Apr 03 2017

Formula

a(n) ~ (7/3)^(1/4) * exp(Pi * sqrt(7*n/3)) / (32 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (7/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017

G.f.: exp(7*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018