A351658 G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)^2) / (1 - x).

1, -1, 0, 2, 3, -8, -61, -134, 567, 6908, 29631, -33857, -1624011, -13579197, -42493684, 449043601, 8591509012, 71167884338, 153434398957, -5188374785607, -95914651874891, -882652244738780, -1819090127593647, 96780404956817315, 2051640887011218601

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

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

Mathematica

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

Crossrefs

Cf. A000587, A125273, A351659.

Sequence in context: A072043 A347289 A095203 * A003096 A333077 A354574

Adjacent sequences: A351655 A351656 A351657 * A351659 A351660 A351661

Keyword

sign

Author

Ilya Gutkovskiy, Feb 16 2022

Status

approved