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

Author

Eric W. Weisstein, Mar 02 2005

Keywords

• nonn
• easy

Links

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

Crossrefs

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).

Programs

Mathematica

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 *)

PARI

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

Formula

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

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Sep 24 2009