A352009 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * a(k) * a(n-2*k-1).

1, 1, 1, -1, -3, -1, 5, 23, 29, -33, -139, -217, 13, 943, 1765, -1545, -8963, -11265, 6229, 73671, 126701, -65713, -567611, -793449, 415197, 4231583, 7471669, -4933529, -37928499, -52823313, 28920485, 346647351, 610476733, -316142785, -2913394667, -4922323705

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-2)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]
nmax = 35; A[_] = 0; Do[A[x_] = 1/(1 - x A[-2 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A015097, A101912, A352010, A352011.

Sequence in context: A140825 A265981 A037280 * A324204 A168611 A357201

Adjacent sequences: A352006 A352007 A352008 * A352010 A352011 A352012

Keyword

sign

Author

Ilya Gutkovskiy, Feb 28 2022

Status

approved