A355130 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (1 - exp(-x))).

1, 1, 4, 42, 1160, 83270, 14923212, 6414048354, 6410464368912, 14565079937500542, 73986188807621474900, 829702542906852010728090, 20340869993779258576653846936, 1081654382501102944417336793863094, 123961854316018592747078219803021082332

Offset: 0

Author

Seiichi Manyama, Jun 20 2022

Keywords

• nonn

Crossrefs

Cf. A354574, A355102, A355132.

Programs

PARI

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

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1) * 2^k * Stirling2(n-1,k) * a(k).

a(n) = n * A355132(n-1) for n>0.