A385945 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+3,3) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 63, 1533, 62736, 3969387, 366744330, 47441881377, 8313978813120, 1921417594566561, 572533956456137424, 215766174031503450885, 101144655173329674617088, 58127411808811103704523775, 40435528907318329027426583376, 33666103690446265067517343384833

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A000272, A156325, A385946, A385947, A385948.

Cf. A385952.

Programs

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..2} binomial(2,k) * x^(k+1)/(k+1)! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.