A346079 G.f. A(x) satisfies: A(x) = x - x^2 * A(x/(1 - x)) / (1 - x).

0, 1, 0, -1, -2, -2, 2, 17, 54, 109, 54, -796, -5000, -19499, -52252, -44617, 577554, 5071906, 27330978, 108557573, 263947354, -453137963, -11252508862, -92193933208, -545809325184, -2441788385255, -6271647457176, 22814756330975, 492197181810550, 4609129908957190

Offset: 0

Author

Ilya Gutkovskiy, Jul 04 2021

Keywords

• sign

Crossrefs

Cf. A000587, A000995, A336970, A346078.

Programs

Mathematica

nmax = 29; A[] = 0; Do[A[x] = x - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 29}]

Formula

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