A293256 G.f.: Product_{m>0} (1 - x^m + 2!*x^(2*m) - 3!*x^(3*m) + 4!*x^(4*m)).

1, -1, 1, -6, 24, 3, -20, -27, 40, -2, -36, -186, 579, -118, 274, -347, 46, -892, 74, -76, 3106, -3192, -1013, -4844, 12276, -752, 2145, -656, 11198, -11160, -2246, -38752, 32106, -24272, 42182, -7533, 36054, -78906, -4482, -164462, 381837, -174346, 21356, -114910

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=4 of A293071.

Cf. A289486.

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(4, 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, 4, (-1)^k*k!*x^(k*m))) + O(x^50)) \\ Michel Marcus, Oct 04 2017