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A297326 a(n) = [x^n] Product_{k>=1} 1/(1 + k*x^k)^n.

%I A297326 #9 Apr 20 2018 10:44:51
%S A297326 1,-1,-1,-1,27,-76,95,-295,2035,-8119,22714,-66793,254223,-988651,
%T A297326 3444055,-11402626,39248691,-141740051,511583207,-1798826901,
%U A297326 6256648862,-22054706773,78889160635,-281698897727,996551999479,-3520566280801,12522382445455,-44731559517301
%N A297326 a(n) = [x^n] Product_{k>=1} 1/(1 + k*x^k)^n.
%H A297326 Alois P. Heinz, <a href="/A297326/b297326.txt">Table of n, a(n) for n = 0..1000</a>
%F A297326 a(n) = A297325(n,n).
%p A297326 f:= proc(n) local k;
%p A297326 coeff(series(mul(1/(1+k*x^k)^n,k=1..n),x,n+1),x,n);
%p A297326 end proc:
%p A297326 map(f, [$0..30]); # _Robert Israel_, Dec 28 2017
%t A297326 Table[SeriesCoefficient[Product[1/(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]
%Y A297326 Main diagonal of A297325.
%Y A297326 Cf. A297322, A297324, A297329.
%K A297326 sign
%O A297326 0,5
%A A297326 _Ilya Gutkovskiy_, Dec 28 2017