A376137 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^k * (k+1)^2 * a(k) * a(n-k-1).

1, 1, -3, -34, 495, 13631, -467404, -23984426, 1490938299, 123999435015, -12164649041259, -1497474725212924, 212746558833692052, 36393896155519042476, -7062273474686464802160, -1603475573855830444120802, 407344895625777134555939139, 118552169162473363108837155199, -38177398083353809033748641523305

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-1)^k (k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[_] = 0; Do[A[x_] = 1/(1 - x A[-x] + 3 x^2 A'[-x] - x^3 A''[-x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A090192, A105523, A376095, A376134, A376135.

Sequence in context: A134491 A045727 A105713 * A380491 A367840 A337388

Adjacent sequences: A376134 A376135 A376136 * A376138 A376139 A376140

Keyword

sign

Author

Ilya Gutkovskiy, Sep 11 2024

Status

approved