cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A355106 E.g.f. A(x) satisfies: A(x) = 1 + 2 * x * A(-log(1-x)).

Original entry on oeis.org

1, 2, 8, 60, 704, 11640, 254736, 7071512, 241414400, 9898632864, 478455967200, 26853032524912, 1728192188667072, 126200480666269984, 10363161616018802080, 949530356895864383280, 96418968027002031636480, 10785892383962319840160640
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} |Stirling1(n-1,k)| * a(k).
a(n) = 2 * n * A355098(n-1) for n>0.

A355205 E.g.f. A(x) satisfies A'(x) = 1 + 2 * A(-log(1-x)).

Original entry on oeis.org

1, 2, 6, 28, 184, 1596, 17508, 235592, 3799736, 72125344, 1587567768, 40027332256, 1144113365576, 36747710168568, 1316192996129064, 52219780699310176, 2281487895137577232, 109193200290592216368, 5698144666408068511472
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2022

Keywords

Crossrefs

Programs

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

Formula

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

A355099 E.g.f. A(x) satisfies A(x) = 1 - 3 * log(1-x) * A(-log(1-x)).

Original entry on oeis.org

1, 3, 21, 249, 4338, 102537, 3123513, 118277037, 5420074248, 294405725628, 18643757033286, 1357970251340601, 112491520189940304, 10497256870300840845, 1094461858289007808209, 126592088471657042694381, 16143127318109911141849896, 2257107645258692949884188932
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*sum(j=1, i, j*abs(stirling(i, j, 1))*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + 3*x*A(x).
a(0) = 1; a(n) = 3 * Sum_{k=1..n} k * |Stirling1(n,k)| * a(k-1).

A355121 E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(-2 * log(1-x)).

Original entry on oeis.org

1, 1, 5, 74, 2778, 248244, 51212444, 23984832416, 25218677193200, 59000757443457072, 304720138059811544048, 3449059394896458379058208, 84991203371449537414272981856, 4532232538284485346856696552505728, 520204832574009673696495358635072488576
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * |Stirling1(n,k)| * a(k-1).
Showing 1-4 of 4 results.