A022593 Expansion of Product_{m>=1} (1+q^m)^29.

1, 29, 435, 4524, 36801, 249980, 1476535, 7792619, 37464346, 166445529, 690898842, 2702690003, 10033022642, 35545708813, 120756549637, 394935306099, 1247670362782, 3818503661392, 11350088407317, 32837741707782, 92652254354675, 255382893501050, 688721602753864

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=29 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^29: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)^29,{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)^29)) \\ G. C. Greubel, Feb 19 2018

PARI

q='q+O('q^99); Vec((eta(q^2)/eta(q))^29) \\ Altug Alkan, May 03 2018

Formula

a(n) ~ (29/3)^(1/4) * exp(Pi * sqrt(29*n/3)) / (65536 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015