A022622 - OEIS

%I #12 Feb 15 2018 08:12:27

%S 1,-27,351,-2952,18279,-90234,376065,-1380861,4603419,-14211732,

%T 41168493,-112989411,296067411,-745157691,1809973404,-4259279106,

%U 9741879531,-21715736634,47285714262,-100777640049,210581729640,-432065248731,871606288422,-1730764207107,3386501241606

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

%H G. C. Greubel, <a href="/A022622/b022622.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ (-1)^n * sqrt(3) * exp(3*Pi*sqrt(n/2)) / (2^(7/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^27, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_