A352006 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 2^k * a(k) * a(n-2*k-1).

1, 1, 1, 3, 5, 11, 21, 59, 117, 283, 597, 1467, 3125, 7387, 16149, 39931, 87541, 207643, 463061, 1107515, 2473909, 5819739, 13132437, 31080571, 70236533, 164315035, 373572693, 875121339, 1991869237, 4639482331, 10599986709, 24765957371, 56617082101

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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, 32}]
nmax = 32; 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. A000621, A015083, A352007, A352008.

Sequence in context: A274938 A283603 A283818 * A004039 A341532 A293338

Adjacent sequences: A352003 A352004 A352005 * A352007 A352008 A352009

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 28 2022

Status

approved