A350456 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 2*x)) / (1 + 2*x).

1, 1, 1, -1, 1, -3, 17, -85, 385, -1767, 8929, -50633, 312705, -2036267, 13794417, -97295069, 717808897, -5549714767, 44868094145, -377741383697, 3298933836033, -29813463964115, 278462029910993, -2685972391332837, 26733375327601281, -274247228584531767

Offset

0,6

Comments

Shifts 2 places left under 2nd-order inverse binomial transform.

Links

Table of n, a(n) for n=0..25.

Formula

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

Mathematica

nmax = 25; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 + 2 x)]/(1 + 2 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] (-2)^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A007472, A009235, A010739, A051139, A351184, A351185, A351186, A351187.

Sequence in context: A318769 A344228 A216681 * A037787 A037668 A119884

Adjacent sequences: A350453 A350454 A350455 * A350457 A350458 A350459

Keyword

sign

Author

Ilya Gutkovskiy, Feb 04 2022

Status

approved