A355099 -id:A355099 - cp's OEIS frontend

A355098 E.g.f. A(x) satisfies A(x) = 1 - 2 * log(1-x) * A(-log(1-x)).

1, 2, 10, 88, 1164, 21228, 505108, 15088400, 549924048, 23922798360, 1220592387496, 72008007861128, 4853864641010384, 370112914857814360, 31651011896528812776, 3013092750843813488640, 317232128940068230592960, 36726669357239166496674080

Offset: 0

Seiichi Manyama, Jun 19 2022

nonn

Cf. A135750, A355099.

Cf. A355106.

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

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

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

A355107 E.g.f. A(x) satisfies: A(x) = 1 + 3 * x * A(-log(1-x)).

Original entry on oeis.org

1, 3, 18, 189, 2988, 65070, 1845666, 65593773, 2838648888, 146342004696, 8832171768840, 615243982098438, 48886929048261636, 4387169287407671856, 440884788552635315490, 49250783623005351369405, 6076420246639538049330288, 823299493223605468234344696

Offset: 0

Seiichi Manyama, Jun 19 2022

nonn

Cf. A354730, A355106.

Cf. A355099.

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

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} |Stirling1(n-1,k)| * a(k).

a(n) = 3 * n * A355099(n-1) for n>0.

cp's OEIS Frontend

A355098 E.g.f. A(x) satisfies A(x) = 1 - 2 * log(1-x) * A(-log(1-x)).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula