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

%I

%S 1,-1,5,-29,270,-3233,47800,-838561,17013991,-391779640,10091836632,

%T -287491284748,8973657413421,-304549220113387,11165193890312790,

%U -439726629957500944,18514829984975265703,-829953080825411342745,39461813340364709540008

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

%H Alois P. Heinz, <a href="/A292567/b292567.txt">Table of n, a(n) for n = 0..386</a>

%F 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 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, (-k)^n,

%p `if`(i>n, 0, b(n-i, i, k))+b(n, i-1, k))

%p end:

%p a:= n-> b(n\$3):

%p seq(a(n), n=0..23);

%t 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 a[n_] := If[n == 0, 1, b[n, n, n]];

%t a /@ Range[0, 23] (* _Jean-François Alcover_, Dec 30 2020, after _Alois P. Heinz_ *)

%Y Cf. A002865, A292462.

%K sign

%O 0,3

%A _Alois P. Heinz_, Sep 19 2017

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Last modified July 27 10:44 EDT 2021. Contains 346304 sequences. (Running on oeis4.)