A355092 -id:A355092 - cp's OEIS frontend

A355083 E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(exp(x) - 1).

1, 2, 10, 86, 1106, 19562, 451014, 13051586, 460907034, 19434738686, 961628831658, 55046140338642, 3602414472002206, 266842000568643866, 22180625837341816898, 2053584526860808500094, 210393497508897167616290, 23715128208081620773251530

Offset: 0

Seiichi Manyama, Jun 19 2022

nonn

Cf. A213357, A355092.

Cf. A355100.

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

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} k * Stirling2(n,k)* a(k-1).

A355101 E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(exp(x) - 1).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Jun 19 2022

nonn

Cf. A048801, A355100.

Cf. A355092.

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;

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.

cp's OEIS Frontend

A355083 E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(exp(x) - 1).

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