A386512 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+3,4) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 3, 52, 3325, 598906, 255199051, 226888865575, 382997189880593, 1140957869006770561, 5659169551911928576531, 44571684957086887771692731, 535930324156886354251195391269, 9517054240482595566592327616630965, 242627830243798770154326313268171970697

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..4} binomial(3,k-1) * x^k/k! * (d^k/dx^k A(x)) ).

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*binomial(j+3, 4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143925, A386510, A386511, A386513.

Cf. A385946, A386454.

Sequence in context: A337755 A263530 A136723 * A202649 A347611 A302932

Adjacent sequences: A386509 A386510 A386511 * A386513 A386514 A386515

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2025

Status

approved