A351184 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 + 3*x)) / (1 + 3*x).

1, 1, 1, -2, 4, -11, 55, -359, 2359, -15230, 100840, -716555, 5580145, -47230091, 425472229, -4013326982, 39379161136, -402010392971, 4279164575167, -47533936734179, 550239127112107, -6618018093867506, 82447377648018700, -1061324336149876667, 14095604842846277617

Offset

0,4

Comments

Shifts 2 places left under 3rd-order inverse binomial transform.

Links

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

Formula

a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * (-3)^k * a(n-k-2).

Mathematica

nmax = 24; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 + 3 x)]/(1 + 3 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] (-3)^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 24}]

Crossrefs

Cf. A010739, A051139, A317996, A350456, A351049, A351185, A351186, A351187.

Sequence in context: A352969 A091233 A173312 * A156434 A007903 A182100

Adjacent sequences: A351181 A351182 A351183 * A351185 A351186 A351187

Keyword

sign

Author

Ilya Gutkovskiy, Feb 04 2022

Status

approved