A293072 G.f.: Product_{m>0} (1-x^m+2!*x^(2*m)).

1, -1, 1, 0, 0, -3, 4, -3, 4, -2, 0, -6, 9, -10, 10, -5, 10, -16, 20, -28, 22, -18, 19, -32, 54, -50, 45, -38, 44, -78, 106, -118, 96, -98, 110, -129, 192, -216, 204, -182, 213, -286, 368, -412, 366, -362, 394, -524, 676, -714, 680, -641, 742, -936, 1170

Offset: 0

Author

Seiichi Manyama, Oct 03 2017

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 501 terms from Seiichi Manyama)

Crossrefs

Column k=2 of A293071.

Cf. A293204, A293304.

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

Mathematica

nmax = 100; CoefficientList[Series[Product[1 - x^k + 2*x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2017 *)

PARI

Vec(prod(m=1, 80, 1-x^m+2*x^(2*m)) + O(x^80)) \\ Michel Marcus, Oct 04 2017