A351187 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 6*x)) / (1 + 6*x).

1, 1, 1, -5, 25, -131, 793, -6137, 60049, -670919, 7930321, -96775853, 1225237609, -16333089227, 232150489129, -3531321746465, 57178717416097, -975918663642767, 17400776511175201, -322309002081819221, 6188520430773389881, -123166171374344928275, 2542231599282355411897

Offset

0,4

Comments

Shifts 2 places left under 6th-order inverse binomial transform.

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * (-6)^k * a(n-k-2).

Mathematica

nmax = 22; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 + 6 x)]/(1 + 6 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] (-6)^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A010739, A051139, A318181, A350456, A351057, A351184, A351185, A351186.

Sequence in context: A102893 A094602 A207834 * A355839 A344396 A351587

Adjacent sequences: A351184 A351185 A351186 * A351188 A351189 A351190

Keyword

sign

Author

Ilya Gutkovskiy, Feb 04 2022

Status

approved