A355101 - OEIS

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A355101

E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(exp(x) - 1).

1, 3, 18, 189, 2952, 63225, 1759374, 61261200, 2595618720, 130963993263, 7734817065600, 527276606418837, 41005535326851456, 3602215645092352314, 354438336568129922052, 38776184401330464272910, 4686507224871009709115232, 622194587177907979874119473

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} Stirling2(n-1,k) * a(k).

a(n) = 3 * n * A355092(n-1) for n>0.

PROG

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*i*sum(j=0, i-1, stirling(i-1, j, 2)*v[j+1])); v;

CROSSREFS

Cf. A048801, A355100.