A355134 -id:A355134 - cp's OEIS frontend

A355209 E.g.f. A(x) satisfies A'(x) = 1 + A(-2 * log(1-x)).

1, 2, 10, 108, 2308, 94384, 7315728, 1077605632, 304189296192, 166216599473344, 177463576125821632, 373017466526422396288, 1552199775052648327045760, 12835792253795957289436533760, 211464475635678910995043533156352

Offset: 1

Seiichi Manyama, Jun 24 2022

nonn

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

Cf. A143805, A355134, A355205.

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

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

A355126 E.g.f. A(x) satisfies: A(x) = 1 + x * A(-2 * log(1-x)).

Original entry on oeis.org

1, 1, 4, 54, 1936, 168780, 34360128, 15979581632, 16740281020160, 39091514910283872, 201702609432140369280, 2281926772696486970224192, 56217269029941735581289119232, 2997472083791372184890466743907712, 344025706673467887482938899075885442048

Offset: 0

Seiichi Manyama, Jun 20 2022

nonn

Cf. A354730, A355106, A355134.

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*abs(stirling(i-1, j, 1))*v[j+1])); v;

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

a(n) = n * A355134(n-1) for n>0.

cp's OEIS Frontend

A355209 E.g.f. A(x) satisfies A'(x) = 1 + A(-2 * log(1-x)).

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