A293236 - OEIS

%I #14 Nov 15 2020 03:10:22

%S 1,-1,1,-6,24,-117,700,-4947,39760,-358682,3594084,-39598866,

%T 475774299,-6191078998,86742689434,-1301964957707,20842304366686,

%U -354473010919852,6382843971860354,-121311619900081996,2426875912883720386,-50976050128395861672

%N G.f.: Product_{i>0} Sum_{j>=0} (-1)^j*j!*x^(j*i).

%H Alois P. Heinz, <a href="/A293236/b293236.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) ~ (-1)^n * n! * (1 - 1/n^2 + 3/n^4 + 12/n^5 + 35/n^6 + 61/n^7 - 153/n^8 - 2197/n^9 - 11330/n^10), for coefficients see A293267. - _Vaclav Kotesovec_, Oct 04 2017

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       add(b(n-i*j, i-1)*j!*(-1)^j, j=0..n/i)))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..23);  # _Alois P. Heinz_, Oct 04 2017

%t m = 22;

%t CoefficientList[Product[Sum[(-1)^j j! x^(i j), {j, 0, m}], {i, 1, m}] + O[x]^m, x] (* _Jean-François Alcover_, Nov 15 2020 *)

%Y Cf. A293071.

%K sign

%O 0,4

%A _Seiichi Manyama_, Oct 03 2017