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.

A355100 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(exp(x) - 1).

Original entry on oeis.org

1, 2, 8, 60, 688, 11060, 234744, 6314196, 208825376, 8296326612, 388694773720, 21155834296476, 1321107368127408, 93662776272057356, 7471576015922028248, 665418775120254506940, 65714704859545872003008, 7153378915302503698953860
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, stirling(i-1, j, 2)*v[j+1])); v;

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} Stirling2(n-1,k) * a(k).
a(n) = 2 * n * A355083(n-1) for n>0.

A355206 E.g.f. A(x) satisfies A'(x) = 1 + 2 * A(exp(x) - 1).

Original entry on oeis.org

1, 2, 6, 26, 154, 1190, 11586, 138338, 1982526, 33510602, 658520330, 14863556590, 381389448738, 11026919584330, 356473786663910, 12798132569470442, 507233393189820394, 22074530128695694286, 1049825961204593354866, 54326220485710633589858
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, stirling(i, j, 2)*v[j])); v;

Formula

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

A355092 E.g.f. A(x) satisfies A(x) = 1 + 3 * (exp(x) - 1) * A(exp(x) - 1).

Original entry on oeis.org

1, 3, 21, 246, 4215, 97743, 2917200, 108150780, 4850518269, 257827235520, 15978078982389, 1139042647968096, 92364503720316726, 8439008013526902906, 861692986696232539398, 97635567184812702273234, 12199893866233489801453323, 1671886886212411035295719261
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*stirling(i, j, 2)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(log(1+x)) = 1 + 3*x*A(x).
a(0) = 1; a(n) = 3 * Sum_{k=1..n} k * Stirling2(n,k)* a(k-1).

A355122 E.g.f. A(x) satisfies A(x) = 1 + (exp(x) - 1) * A(2 * (exp(x) - 1)).

Original entry on oeis.org

1, 1, 5, 73, 2725, 242921, 50068197, 23441365641, 24644653272869, 57655911504114985, 297771560486880287589, 3370400630994211122517705, 83052841013576647141181337509, 4428866659075152490151174819022697, 508340576698412171558866359984025695205
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)*stirling(i, j, 2)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(log(1+x)) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * Stirling2(n,k) * a(k-1).
Showing 1-4 of 4 results.