A355131 -id:A355131 - cp's OEIS frontend

A355210 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (exp(x) - 1)).

1, 2, 10, 106, 2234, 90570, 6986490, 1026623306, 289475035770, 158101579596106, 168768027732007674, 354715566244066506058, 1476006372586517922472826, 12205618234758923312503183690, 201082085503026084194089831880698

Offset: 1

Seiichi Manyama, Jun 24 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..81

Cf. A003659, A355131, A355206.

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

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

A355128 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (exp(x) - 1)).

Original entry on oeis.org

1, 1, 4, 54, 1928, 167770, 34128972, 15867798142, 16621680303888, 38813463431274402, 200266228576991017940, 2265670919773168963168454, 55816752493202168837392763544, 2976116188645489878229876218205674, 341574630434025162744892242114482410332

Offset: 0

Seiichi Manyama, Jun 20 2022

nonn

Cf. A048801, A355100, A355131.

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

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

a(n) = n * A355131(n-1) for n>0.

cp's OEIS Frontend

A355210 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (exp(x) - 1)).

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