A355093 E.g.f. A(x) satisfies A(x) = 1 + 2 * (1 - exp(-x)) * A(1 - exp(-x)).

1, 2, 6, 14, -50, -838, 1730, 136530, -486826, -53845210, 608573414, 39761626434, -1250658124134, -39125693738246, 3470290682698798, 1980500546819286, -11592469556319388642, 475984934077375262394, 35772633977318034763762

Offset: 0

Author

Seiichi Manyama, Jun 19 2022

Keywords

• sign

Crossrefs

Cf. A353177, A355094.

Cf. A355102.

Programs

PARI

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

Formula

E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + 2*x*A(x).

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