A355122 -id:A355122 - cp's OEIS frontend

A355131 E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(2 * (exp(x) - 1)).

1, 2, 18, 482, 33554, 5688162, 2266828306, 2077710037986, 4312607047919378, 20026622857699101794, 205970083615742633015314, 4651396041100180736449396962, 228932014511191529094605862938898, 24398187888144654481778017293891600738

Offset: 0

Seiichi Manyama, Jun 20 2022

nonn

Cf. A355122, A355128.

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

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

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

A355216 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (exp(x) - 1))/2.

Original entry on oeis.org

1, 1, 3, 19, 239, 5675, 249983, 20404811, 3112376543, 898693573515, 498042936169343, 536255530818837835, 1132713758105613132319, 4726517343060928547800331, 39145565125819857567685815231, 645447728030234045716450604490955

Offset: 1

Seiichi Manyama, Jun 24 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..82

Cf. A355122, A355210.

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

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

cp's OEIS Frontend

A355131 E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(2 * (exp(x) - 1)).

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