A022591 Expansion of Product_{m>=1} (1+q^m)^27.

1, 27, 378, 3681, 28134, 180144, 1005957, 5032422, 22986801, 97229361, 384953553, 1438738443, 5110502256, 17348445108, 56541857409, 177611637141, 539501563962, 1589134470966, 4550281700055, 12692702415312, 34556103662778, 91975719684573, 239686155975618

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=27 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^27: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)^27,{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)^27)) \\ G. C. Greubel, Feb 19 2018

Formula

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