A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(3*k) * a(n-1-3*k).

1, 1, 1, 1, 2, 6, 16, 52, 234, 1018, 4724, 27864, 166816, 1018096, 7421220, 56215420, 427276280, 3714931512, 33908654224, 309043657936, 3126424467816, 33317327728936, 354276443249552, 4093007897140128, 49813497858533344, 605442506092221760, 7871720463184084560

Offset

0,5

Links

Table of n, a(n) for n=0..26.

Formula

E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(w*x) + A(w^2*x))/3, where w = exp(2*Pi*i/3).

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)\3, binomial(i-1, 3*j)*v[3*j+1]*v[i-3*j])); v;

Crossrefs

Cf. A000111, A000142, A386203.

Cf. A124753, A385691.

Sequence in context: A263595 A263596 A263591 * A218779 A241066 A045696

Adjacent sequences: A386199 A386200 A386201 * A386203 A386204 A386205

Keyword

nonn

Author

Seiichi Manyama, Jul 14 2025

Status

approved