A336970 G.f. A(x) satisfies: A(x) = 1 - x^2 * A(x/(1 - x)) / (1 - x).

1, 0, -1, -1, 0, 3, 9, 16, 7, -87, -472, -1567, -3375, -216, 45927, 308107, 1372744, 4351599, 5711849, -49345432, -547773585, -3517370859, -16914970464, -56474505155, -25470754271, 1593389360016, 17323737305039, 125785962635543, 706598399399184

Offset: 0

Author

Ilya Gutkovskiy, Aug 09 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..657

Crossrefs

Cf. A000587, A000994, A336971.

Programs

Mathematica

nmax = 28; A[] = 0; Do[A[x] = 1 - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]

Formula

a(0) = 1, a(1) = 0; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).