A138564 -id:A138564 - cp's OEIS frontend

A104344 a(n) = Sum_{k=1..n} k!^2.

1, 5, 41, 617, 15017, 533417, 25935017, 1651637417, 133333531817, 13301522971817, 1606652445211817, 231049185247771817, 39006837228880411817, 7639061293780877851817, 1717651314017980301851817, 439480788011413032845851817, 126953027293558583218061851817

Offset: 1

Eric W. Weisstein, Mar 02 2005

Seiichi Manyama, Table of n, a(n) for n = 1..253
Eric Weisstein's World of Mathematics, Factorial Sums

Cf. A001044, A061062, A100289.

Sum_{k=1..n} (k!)^m: A007489 (m=1), this sequence (m=2), A138564 (m=3), A289945 (m=4), A316777 (m=5), A289946 (m=6).

Table[Sum[(k!)^2,{k,n}],{n,15}] (* Harvey P. Dale, Jul 21 2011 *)
Accumulate[(Range[20]!)^2] (* Much more efficient than the above program. *) (* Harvey P. Dale, Aug 15 2022 *)

a(n) = sum(k=1, n, k!^2); \\ Michel Marcus, Jul 16 2017

a(n) = A061062(n) - 1. - Michel Marcus, Feb 28 2014

More terms from Vladimir Joseph Stephan Orlovsky, Sep 24 2009

A316777 a(n) = Sum_{k=1..n} (k!)^5.

Original entry on oeis.org

1, 33, 7809, 7970433, 24891170433, 193516654370433, 3252209580756770433, 106565314598088199970433, 6292489787293574101716770433, 629244614687684894925781716770433, 101340090272908294280184341461716770433, 25216602106682627624613336066827221716770433

Offset: 1

Seiichi Manyama, Aug 03 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..120
Eric Weisstein's World of Mathematics, Factorial Sums

Sum_{k=1..n} (k!)^m: A007489 (m=1), A104344 (m=2), A138564 (m=3), A289945 (m=4), this sequence (m=5), A289946 (m=6).

Accumulate[(Range[15]!)^5] (* Harvey P. Dale, Jan 24 2021 *)

PARI
```
{a(n) = sum(k=1, n, k!^5)}
```

A339311 a(n) = Sum_{k=1..n} (k!)^n.

Original entry on oeis.org

1, 5, 225, 333089, 24891170433, 139317055679149697, 82606511560391889386751489, 6984964663477899063759529684476994049, 109110688697205077023425816926479750793809817618433, 395940866162019279867473563258123776010342586429441374123441432577

Offset: 1

Seiichi Manyama, Nov 29 2020

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..30

Sum_{k=1..n} (k!)^m: A007489 (m=1), A104344 (m=2), A138564 (m=3), A289945 (m=4), A316777 (m=5), A289946 (m=6).

Cf. A000142, A112999.

a[n_] := Sum[(k!)^n, {k, 1, n}]; Array[a, 10] (* Amiram Eldar, Apr 28 2021 *)

PARI
```
{a(n) = sum(k=1, n, k!^n)}
```

cp's OEIS Frontend

A104344 a(n) = Sum_{k=1..n} k!^2.

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A316777 a(n) = Sum_{k=1..n} (k!)^5.

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Mathematica

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A339311 a(n) = Sum_{k=1..n} (k!)^n.

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Author

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Programs

Mathematica

PARI