A385322 E.g.f. A(x) satisfies A(x) = exp(x + x^2/2 * A'(x)).

1, 1, 2, 10, 94, 1386, 29146, 822928, 29927612, 1359897724, 75429391276, 5013317213136, 393252908602720, 35947138247529952, 3787896504780614864, 455830291523748797776, 62132218311858089750416, 9523376536749853754046864, 1630878867943272798422352400, 310238352508716702644975872192

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = a(n-1) + (1/2) * Sum_{k=0..n-1} (1 + k) * k * 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)*j*binomial(i-1, j)*v[j+1]*v[i-j])/2); v;

Crossrefs

Cf. A386531, A386532.

Cf. A143925, A156325.

Sequence in context: A100622 A355782 A103436 * A182173 A385985 A362643

Adjacent sequences: A385319 A385320 A385321 * A385323 A385324 A385325

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2025

Status

approved