A357179 Expansion of Product_{k>=1} (1 - x^k)^Fibonacci(k).

1, -1, -1, -1, -1, 0, -1, 2, 1, 5, 6, 14, 15, 32, 40, 64, 86, 131, 166, 237, 287, 362, 389, 368, 149, -339, -1477, -3680, -7827, -15245, -28270, -50493, -87886, -149827, -250966, -414542, -675741, -1089267, -1736640, -2741788, -4284837, -6632751, -10162683, -15412613, -23110653, -34236290

Offset: 0

Author

Ilya Gutkovskiy, Oct 02 2022

Keywords

• sign

Comments

Convolution inverse of A166861.

Crossrefs

Cf. A000045, A166861, A261050, A357475.

Programs

Mathematica

nmax = 45; CoefficientList[Series[Product[(1 - x^k)^Fibonacci[k], {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Sum[d Fibonacci[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 45}]