A386502 E.g.f. A(x) satisfies A(x) = exp(x + x^4*A'''(x)).

1, 1, 1, 1, 25, 3121, 1141921, 967142401, 1632504592321, 4951351715986369, 25004252825639317441, 198308457113999900437441, 2358282522829655305887600961, 40498770303734530275747011026561, 973509226030256545543333641850364737, 31906760631850274511535853878168004240641

Offset

0,5

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * (2*k - 3*k^2 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).

a(n) == 1 (mod 24). - Hugo Pfoertner, Jul 24 2025

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)*sum(k=1, 3, stirling(3, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143925, A385066, A386503, A386504.

Cf. A385921, A386449.

Sequence in context: A075414 A385846 A386450 * A226277 A013737 A018861

Adjacent sequences: A386499 A386500 A386501 * A386503 A386504 A386505

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2025

Status

approved