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.

A356788 E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x)^2.

Original entry on oeis.org

1, 0, 2, 3, 88, 485, 13896, 158767, 4919664, 90698841, 3130084360, 81025744811, 3144372342552, 104942286748741, 4582896912897408, 186591555463556895, 9135453970592830816, 437146665470130792497, 23852990622867670807704, 1307029600226135900982835
Offset: 0

Views

Author

Seiichi Manyama, Aug 27 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (n+k+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n+k+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.

A357347 E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(2 * A(x)).

Original entry on oeis.org

0, 1, 7, 103, 2385, 75756, 3064239, 150689953, 8729691693, 582299930167, 43956280309659, 3704637865439380, 344825037782332457, 35131983926187957173, 3888817094785288023367, 464724955485177444101895, 59631976064836824117227621, 8177487264101392841050876136
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (n+2*k)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=1..n} (n+2*k)^(k-1) * Stirling2(n,k).
E.g.f.: Series_Reversion( exp(-x) * log(1 + x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024

A355763 E.g.f. satisfies A(x)^2 * log(A(x)) = exp(x*A(x)) - 1.

Original entry on oeis.org

1, 1, 0, 5, -13, 207, -1791, 28849, -438600, 8619291, -181134313, 4381744589, -115439041983, 3356162869607, -105668550658100, 3600058076291465, -131618721053773713, 5146452228945999699, -214171122214841864975, 9454288479242533668837
Offset: 0

Views

Author

Seiichi Manyama, Jul 16 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (n-2*k+1)^(k-1)*stirling(n, k, 2));

Formula

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

A367201 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.

Original entry on oeis.org

1, 1, 10, 200, 6167, 258607, 13748744, 886397829, 67211684890, 5861684458896, 578088714806497, 63617223837958309, 7728596914020856162, 1027393177458209939977, 148344954037140113652010, 23119776330887635387231580, 3868359765874829925197165527
Offset: 0

Views

Author

Seiichi Manyama, Nov 10 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (n+3*k+1)^(k-1) * Stirling2(n,k).
Showing 1-4 of 4 results.