A385980 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+3,3) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 9, 295, 24921, 4504516, 1543745107, 919392117722, 890353538984905, 1330464112593541120, 2940642877993896450701, 9284167814032856189142864, 40666099850492306669400356041, 241073945237343019120798232332320, 1893421587381601800604423881821405775

Offset

0,3

Links

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

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..3} binomial(3,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.

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

Crossrefs

Cf. A000272, A156326, A385979, A385981, A385982.

Cf. A385946, A385952.

Sequence in context: A053935 A332129 A086699 * A027834 A175823 A129934

Adjacent sequences: A385977 A385978 A385979 * A385981 A385982 A385983

Keyword

nonn

Author

Seiichi Manyama, Jul 14 2025

Status

approved