A293236 G.f.: Product_{i>0} Sum_{j>=0} (-1)^j*j!*x^(j*i).

1, -1, 1, -6, 24, -117, 700, -4947, 39760, -358682, 3594084, -39598866, 475774299, -6191078998, 86742689434, -1301964957707, 20842304366686, -354473010919852, 6382843971860354, -121311619900081996, 2426875912883720386, -50976050128395861672

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

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

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*j!*(-1)^j, j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 04 2017

Mathematica

m = 22;
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 *)

Crossrefs

Cf. A293071.

Sequence in context: A273813 A293257 A223752 * A217193 A109583 A377502

Adjacent sequences: A293233 A293234 A293235 * A293237 A293238 A293239

Keyword

sign

Author

Seiichi Manyama, Oct 03 2017

Status

approved