A352010 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-3)^k * a(k) * a(n-2*k-1).

1, 1, 1, -2, -5, 1, 16, 94, 127, -317, -1103, -2258, 160, 18922, 39664, -163064, -524489, -187577, 1711591, 12353800, 18926119, -53449661, -207918068, -15689834, 960812728, 3295064650, 3870965368, -33248209286, -96830084768, 17122290256, 505711364524

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-3)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[_] = 0; Do[A[x_] = 1/(1 - x A[-3 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A015098, A101912, A352009, A352011.

Sequence in context: A121579 A214733 A106852 * A350016 A162975 A350015

Adjacent sequences: A352007 A352008 A352009 * A352011 A352012 A352013

Keyword

sign

Author

Ilya Gutkovskiy, Feb 28 2022

Status

approved