A386203 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(4*k) * a(n-1-4*k).

1, 1, 1, 1, 1, 2, 7, 22, 57, 184, 949, 4984, 21649, 99728, 659443, 4777648, 29500593, 179618176, 1441372201, 13153104256, 105727977601, 808208897792, 7631709900607, 83311277669632, 825548919414057, 7638849184574464, 83126488334117149, 1050853652511099904

Offset

0,6

Links

Table of n, a(n) for n=0..27.

Formula

E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(i*x) + A(-x) + A(-i*x))/4, where i is the imaginary unit.

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, binomial(i-1, 4*j)*v[4*j+1]*v[i-4*j])); v;

Crossrefs

Cf. A000111, A000142, A386202.

Cf. A118968, A385725.

Sequence in context: A369444 A371716 A063019 * A369845 A365756 A183156

Adjacent sequences: A386200 A386201 A386202 * A386204 A386205 A386206

Keyword

nonn

Author

Seiichi Manyama, Jul 14 2025

Status

approved