A355120 -id:A355120 - cp's OEIS frontend

A355133 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(2 * log(1+x)).

1, 2, 14, 292, 16836, 2517888, 927979616, 811623678304, 1639230314891936, 7494183556478948928, 76401967141928846136512, 1716972732272402536841957760, 84279193103775042893631925450624, 8968818994749615710061662692132983296

Offset: 0

Seiichi Manyama, Jun 20 2022

nonn

Cf. A354728, A355120, A355124.

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, 1)*v[j])); v;

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

a(0) = 1; a(n) = Sum_{k=1..n} k * 2^k * Stirling1(n,k) * a(k-1).

A355214 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * log(1+x))/2.

Original entry on oeis.org

1, 1, 1, 0, -8, -64, -600, -14104, -1170120, -248815984, -115219852880, -111345726833056, -220485042541083808, -885633596688107274496, -7173767949430448755993856, -116777715174661360994951467008, -3812515511649504447203183936705536

Offset: 1

Seiichi Manyama, Jun 24 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 1..83

Cf. A355120, A355208.

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, 1)*v[j])); v;

a(1) = 1; a(n+1) = Sum_{k=1..n} 2^(k-1) * Stirling1(n,k) * a(k).

cp's OEIS Frontend

A355133 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(2 * log(1+x)).

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