A355101 - OEIS

%I #10 Jun 19 2022 08:40:41

%S 1,3,18,189,2952,63225,1759374,61261200,2595618720,130963993263,

%T 7734817065600,527276606418837,41005535326851456,3602215645092352314,

%U 354438336568129922052,38776184401330464272910,4686507224871009709115232,622194587177907979874119473

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

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

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

%o (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;

%Y Cf. A048801, A355100.

%Y Cf. A355092.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 19 2022