A293257 G.f.: Product_{m>0} (1 - x^m + 2!*x^(2*m) - 3!*x^(3*m) + 4!*x^(4*m) - 5!*x^(5*m)).

1, -1, 1, -6, 24, -117, -20, 93, 160, -122, -156, 414, 459, -2038, -2486, 13333, 1246, 2468, -8446, -13036, -4814, 7848, -11453, 50116, -46764, -1952, -164895, 214144, 249038, 396600, -1598966, 254048, -465174, -559712, 726422, 747, 1067574, 2897334, 165438

Offset: 0

Author

Seiichi Manyama, Oct 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Column k=5 of A293071.

Cf. A293250.

Programs

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..min(5, n/i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);  # Alois P. Heinz, Oct 04 2017

PARI

Vec(prod(m=1, 50, 1+sum(k=1, 5, (-1)^k*k!*x^(k*m))) + O(x^50)) \\ Michel Marcus, Oct 04 2017