login
a(n) = [x^n] Product_{k>=1} 1/(1 + k*x^k)^n.
6

%I #9 Apr 20 2018 10:44:51

%S 1,-1,-1,-1,27,-76,95,-295,2035,-8119,22714,-66793,254223,-988651,

%T 3444055,-11402626,39248691,-141740051,511583207,-1798826901,

%U 6256648862,-22054706773,78889160635,-281698897727,996551999479,-3520566280801,12522382445455,-44731559517301

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

%H Alois P. Heinz, <a href="/A297326/b297326.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A297325(n,n).

%p f:= proc(n) local k;

%p coeff(series(mul(1/(1+k*x^k)^n,k=1..n),x,n+1),x,n);

%p end proc:

%p map(f, [$0..30]); # _Robert Israel_, Dec 28 2017

%t Table[SeriesCoefficient[Product[1/(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

%Y Main diagonal of A297325.

%Y Cf. A297322, A297324, A297329.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Dec 28 2017