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A292567 a(n) = [x^n] 1/(1+n*x) * Product_{j=2..n} 1/(1-x^j).

%I A292567 #15 Dec 30 2020 08:22:20
%S A292567 1,-1,5,-29,270,-3233,47800,-838561,17013991,-391779640,10091836632,
%T A292567 -287491284748,8973657413421,-304549220113387,11165193890312790,
%U A292567 -439726629957500944,18514829984975265703,-829953080825411342745,39461813340364709540008
%N A292567 a(n) = [x^n] 1/(1+n*x) * Product_{j=2..n} 1/(1-x^j).
%H A292567 Alois P. Heinz, <a href="/A292567/b292567.txt">Table of n, a(n) for n = 0..386</a>
%F A292567 a(n) ~ (-1)^n * n^n * (1 + 1/n^2 - 1/n^3 + 2/n^4 - 2/n^5 + 4/n^6 - 4/n^7 + 7/n^8 - 8/n^9 + 12/n^10), for coefficients see A002865. - _Vaclav Kotesovec_, Sep 19 2017
%p A292567 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, (-k)^n,
%p A292567       `if`(i>n, 0, b(n-i, i, k))+b(n, i-1, k))
%p A292567     end:
%p A292567 a:= n-> b(n$3):
%p A292567 seq(a(n), n=0..23);
%t A292567 b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, (-k)^n, If[i > n, 0, b[n - i, i, k]] + b[n, i - 1, k]];
%t A292567 a[n_] := If[n == 0, 1, b[n, n, n]];
%t A292567 a /@ Range[0, 23] (* _Jean-François Alcover_, Dec 30 2020, after _Alois P. Heinz_ *)
%Y A292567 Cf. A002865, A292462.
%K A292567 sign
%O A292567 0,3
%A A292567 _Alois P. Heinz_, Sep 19 2017