A022594 Expansion of Product_{m>=1} (1+q^m)^30.

1, 30, 465, 4990, 41820, 292236, 1773325, 9603210, 47322525, 215286380, 914269641, 3656192760, 13865226845, 50148901590, 173821904265, 579696375972, 1866529110420, 5819476726230, 17613901516660, 51870170192610, 148909462006422, 417468856858550, 1144709400114480

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=30 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^30: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)^30,{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)^30)) \\ G. C. Greubel, Feb 19 2018

Formula

a(n) ~ (5/2)^(1/4) * exp(Pi * sqrt(10*n)) / (65536 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015