A022592 Expansion of Product_{m>=1} (1+q^m)^28.

1, 28, 406, 4088, 32249, 212772, 1222438, 6283400, 29454432, 127721972, 517920340, 1980864312, 7194850761, 24957519216, 83064794746, 266299577040, 825106028411, 2477872472348, 7230302637376, 20543975496576, 56949757063171, 154281017250160, 409072030569524

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=28 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^28:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 19 2018

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^28,{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)^28)) \\ G. C. Greubel, Feb 19 2018

Formula

a(n) ~ (7/3)^(1/4) * exp(2 * Pi * sqrt(7*n/3)) / (32768 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015