A351659 G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)^2) / (1 - x)^2.

1, -1, -1, 2, 10, 10, -97, -638, -1316, 9908, 118713, 560533, -697429, -38229322, -364288567, -1441996161, 11586777849, 281338444108, 2772828770441, 10249821640498, -170439385810217, -4104012197171264, -46232949019802137, -204897893603728741, 3708422726478663919

Offset: 0

Author

Ilya Gutkovskiy, Feb 16 2022

Keywords

• sign

Crossrefs

Cf. A000587, A014619, A125274, A351658.

Programs

Mathematica

nmax = 24; A[] = 0; Do[A[x] = 1 - x A[x/(1 - x)^2]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n + k, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]

Formula

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