A352008 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * a(k) * a(n-2*k-1).

1, 1, 1, 5, 9, 29, 65, 437, 953, 3981, 10097, 49829, 123241, 516349, 1400737, 10203285, 24698905, 111642477, 304787665, 1704790917, 4392726473, 19951366877, 56296655617, 336083829621, 878995865721, 3974885167949, 11362790432305, 60789762148453, 165051865924137

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(4*x^2)).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[4^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 28}]
nmax = 28; A[_] = 0; Do[A[x_] = 1/(1 - x A[4 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000621, A015085, A352006, A352007.

Sequence in context: A191013 A193487 A006131 * A270595 A303988 A242329

Adjacent sequences: A352005 A352006 A352007 * A352009 A352010 A352011

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 28 2022

Status

approved