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.

A368769 a(n) = (n!)^3 * Sum_{k=1..n} 1/(k!)^3.

Original entry on oeis.org

0, 1, 9, 244, 15617, 1952126, 421659217, 144629111432, 74050105053185, 53982526583771866, 53982526583771866001, 71850742883000353647332, 124158083701824611102589697, 272775309892908670592389564310, 748495450346141392105516964466641
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[(n!)^3 Sum[1/(k!)^3,{k,n}],{n,0,20}] (* Harvey P. Dale, May 11 2025 *)
  • PARI
    a(n) = n!^3*sum(k=1, n, 1/k!^3);

Formula

a(0) = 0; a(n) = n^3 * a(n-1) + 1.
a(n) = A217284(n) - (n!)^3.
a(n) ~ (A271574 - 1) * (n!)^3. - Vaclav Kotesovec, Jan 05 2024

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.

A368772 a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.

Original entry on oeis.org

0, 1, 16, 459, 29440, 3680125, 794907216, 272653175431, 139598425821184, 101767252423643865, 101767252423643866000, 135452212975869985647331, 234061424022303335198589696, 514232948577000427431301564309, 1411055210895289172871491492466640
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Programs

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

Formula

a(0) = 0; a(n) = n^3 * a(n-1) + n^3.
a(n) = n^3 * A217284(n-1) for n > 0.
a(n) = Sum_{k=1..n} (k!*binomial(n,k))^3. - Ridouane Oudra, Jun 14 2025

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.
Showing 1-4 of 4 results.