A022609 - OEIS

%I #12 Apr 05 2017 09:50:10

%S 1,-14,91,-378,1197,-3290,8386,-20008,44800,-95578,196679,-391692,

%T 756798,-1424934,2624119,-4735878,8388919,-14611226,25065397,

%U -42400456,70790195,-116765126,190454404,-307408346,491306907

%N Expansion of Product_{m>=1} (1+q^m)^(-14).

%H Seiichi Manyama, <a href="/A022609/b022609.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(0) = 1, a(n) = -(14/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 05 2017

%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^14, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_