A385548 E.g.f. A(x) satisfies A(x) = 1 + Sum_{k>=1} k * x^k/k! * A(k*x).

1, 1, 4, 27, 340, 7185, 254046, 14579341, 1345796824, 196990674705, 45358607173690, 16288829003062341, 9064769868554283060, 7771093242706161635449, 10211642577081863563621990, 20477419392449457003138477885, 62420691099194078521450782932656

Offset: 0

Author

Seiichi Manyama, Jul 03 2025

Keywords

• nonn

Crossrefs

Cf. A385544.

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

Formula

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