A346078 G.f. A(x) satisfies: A(x) = 1 + x - x^2 * A(x/(1 - x)) / (1 - x).

1, 1, -1, -2, -2, 1, 11, 33, 61, 22, -418, -2363, -8375, -19715, -6325, 263490, 1950298, 9423505, 33042827, 59212141, -283826231, -3970508822, -28167479326, -148668438363, -571280079455, -848399025239, 11052089847863, 148600718966518, 1198795581209734

Offset: 0

Author

Ilya Gutkovskiy, Jul 04 2021

Keywords

• sign

Crossrefs

Cf. A000587, A007476, A336970, A346079.

Programs

Mathematica

nmax = 28; A[] = 0; Do[A[x] = 1 + x - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 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) = a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).