A385066 E.g.f. A(x) satisfies A(x) = exp(x + x^3*A''(x)).

1, 1, 1, 7, 193, 12481, 1570201, 340513321, 117098181313, 60060238918849, 43839052690362481, 43879747204367814961, 58445034533293136385361, 101048138430710700967252945, 222098609829790469135187472009, 609650270727758340550662998605801, 2058153076335502227178904191401488641

Offset

0,4

Links

Table of n, a(n) for n=0..16.

Formula

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

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, 2, stirling(2, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143925, A386502, A386503, A386504.

Cf. A385920, A386448.

Sequence in context: A024096 A030257 A159826 * A012849 A390935 A308610

Adjacent sequences: A385063 A385064 A385065 * A385067 A385068 A385069

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2025

Status

approved