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.

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

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.

A368775 a(n) = (n+1) * (n!)^3 * Sum_{k=0..n} 1/((k+1) * (k!)^3).

Original entry on oeis.org

1, 3, 37, 1333, 106641, 15996151, 4031030053, 1580163780777, 910174337727553, 737241213559317931, 810965334915249724101, 1177521666296942599394653, 2204320559307876546066790417, 5215422443322435907994026126623
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2024

Keywords

Crossrefs

Programs

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

Formula

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

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

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 1-3 of 3 results.