A022612 - OEIS

%I #13 Apr 05 2017 09:50:46

%S 1,-17,136,-697,2669,-8517,24361,-64549,160140,-375564,842078,

%T -1818932,3800537,-7709449,15239497,-29440226,55697542,-103382254,

%U 188589925,-338602243,599066162,-1045509435,1801660255,-3068201310

%N Expansion of Product_{m>=1} (1+q^m)^(-17).

%H Seiichi Manyama, <a href="/A022612/b022612.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (-1)^n * 17^(1/4) * exp(Pi*sqrt(17*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015

%F a(0) = 1, a(n) = -(17/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)^17, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_