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 1-5 of 5 results.

A368770 a(n) = (n!)^3 * Sum_{k=0..n} k/(k!)^3.

Original entry on oeis.org

0, 1, 10, 273, 17476, 2184505, 471853086, 161845608505, 82864951554568, 60408549683280081, 60408549683280081010, 80403779628445787824321, 138937731197954321360426700, 305246195441905644028857459913, 837595560292589087215184870001286
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2024

Keywords

Crossrefs

Cf. A368769, A368771, A368772.
Cf. A180255, A368776.

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.
a(n) = n * A368776(n-1) for n > 0.

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

Cf. A368769, A368770, A368772.
Cf. A368775.

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

Cf. A368769, A368770, A368771.
Cf. A193563, A217284.

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

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

Cf. A368769, A368789.
Cf. A368775.

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.

A368789 a(n) = (n+1)^2 * (n!)^3 * Sum_{k=1..n} 1/((k+1)^2 * (k!)^3).

Original entry on oeis.org

0, 1, 19, 913, 91301, 16434181, 4831649215, 2164578848321, 1402647093712009, 1262382384340808101, 1527482685052377802211, 2419532573122966438702225, 4906812058293375937688112301, 12502557124531521889229310142949
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Cf. A368769, A368788.
Cf. A368776.

Programs

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

Formula

a(0) = 0; a(n) = (n+1)^2 * n * a(n-1) + 1.
a(n) = A368776(n) - (n+1)^2 * (n!)^3.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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