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 1-3 of 3 results.

A368771 a(n) = (n!)^3 * Sum_{k=0..n} k^2/(k!)^3.

Original entry on oeis.org

0, 1, 12, 333, 21328, 2666025, 575861436, 197520472597, 101130481969728, 73724121355931793, 73724121355931793100, 98126805524745216616221, 169563119946759734312830032, 372530174523031136285287580473, 1022222798891197437966829120818108
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!^3*sum(k=0, n, k^2/k!^3);

Formula

a(0) = 0; a(n) = n^3 * a(n-1) + n^2.
a(n) = n^2 * A368775(n-1) for n > 0.

A368776 a(n) = (n+1)^2 * (n!)^3 * Sum_{k=0..n} 1/((k+1)^2 * (k!)^3).

Original entry on oeis.org

1, 5, 91, 4369, 436901, 78642181, 23120801215, 10358118944321, 6712061075920009, 6040854968328008101, 7309434511676889802211, 11578144266496193446702225, 23480476572454280309912112301, 59828254306613506229656062142949
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = (n+1)^2 * n * a(n-1) + 1.

A368788 a(n) = (n+1) * (n!)^3 * Sum_{k=1..n} 1/((k+1) * (k!)^3).

Original entry on oeis.org

0, 1, 13, 469, 37521, 5628151, 1418294053, 555971268777, 320239450815553, 259393955160597931, 285333350676657724101, 414304025182507015394653, 775577135141653132818790417, 1835015501745151312249258126623
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = (n+1)*n!^3*sum(k=1, n, 1/((k+1)*k!^3));

Formula

a(0) = 0; a(n) = (n+1) * n^2 * a(n-1) + 1.
a(n) = A368775(n) - (n+1) * (n!)^3.
Showing 1-3 of 3 results.