%I #15 Sep 08 2022 08:44:46

%S 1,27,378,3681,28134,180144,1005957,5032422,22986801,97229361,

%T 384953553,1438738443,5110502256,17348445108,56541857409,177611637141,

%U 539501563962,1589134470966,4550281700055,12692702415312,34556103662778,91975719684573,239686155975618

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

%H G. C. Greubel, <a href="/A022591/b022591.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ sqrt(3) * exp(3 * Pi * sqrt(n)) / (32768 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015

%t nmax=50; CoefficientList[Series[Product[(1+q^m)^27,{m,1,nmax}],{q,0,nmax}],q] (* _Vaclav Kotesovec_, Mar 05 2015 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^27)) \\ _G. C. Greubel_, Feb 19 2018

%o (Magma) Coefficients(&*[(1+x^m)^27:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 19 2018

%Y Column k=27 of A286335.

%K nonn

%O 0,2

%A _N. J. A. Sloane_