A061062 Sum of squared factorials: (0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2.

1, 2, 6, 42, 618, 15018, 533418, 25935018, 1651637418, 133333531818, 13301522971818, 1606652445211818, 231049185247771818, 39006837228880411818, 7639061293780877851818, 1717651314017980301851818

Offset: 0

Author

Jason Earls, May 27 2001

Keywords

• nonn

Comments

There is a Kurepa-like conjecture (see A049782) for this sequence: for primes p>3, p does not divide a(p-1). However, the conjecture fails for p=20879. - T. D. Noe, Dec 08 2004

Examples

			a(2) = 0!*0! + 1!*1! + 2!*2! = 6.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..253 (terms 0..100 from Harry J. Smith)

Crossrefs

Cf. A001044, A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2), A104344 (if sum starts at k=1), A049782.

Programs

Maple

A061062:=n->sum((k!)^2, k=0..n): seq(A061062(n), n=0..15); # Zerinvary Lajos, Jan 22 2008

Mathematica

s=0; Table[s=s+(n!)^2, {n, 0, 20}]
Accumulate[(Range[0,20]!)^2] (* Harvey P. Dale, Apr 19 2015 *)

PARI

{ a=0; for (n=0, 100, write("b061062.txt", n, " ", a+=(n!)^2) ) } \\ Harry J. Smith, Jul 17 2009

Formula

a(n) = sum(k=0...n, (n-k)!^2 ). - Ross La Haye, Sep 21 2004

Recurrence: a(0) = 1, a(1) = 2, a(n) = (n^2+1)*a(n-1) - n^2*a(n-2). - Vladimir Reshetnikov, Oct 28 2015

Extensions

More terms from T. D. Noe, Dec 08 2004