A061062 - OEIS

%I #37 Dec 15 2017 17:35:01

%S 1,2,6,42,618,15018,533418,25935018,1651637418,133333531818,

%T 13301522971818,1606652445211818,231049185247771818,

%U 39006837228880411818,7639061293780877851818,1717651314017980301851818

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

%C 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

%H Seiichi Manyama, <a href="/A061062/b061062.txt">Table of n, a(n) for n = 0..253</a> (terms 0..100 from Harry J. Smith)

%F a(n) = sum(k=0...n, (n-k)!^2 ). - _Ross La Haye_, Sep 21 2004

%F 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

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

%p A061062:=n->sum((k!)^2, k=0..n): seq(A061062(n), n=0..15); # _Zerinvary Lajos_, Jan 22 2008

%t s=0; Table[s=s+(n!)^2, {n, 0, 20}]

%t Accumulate[(Range[0,20]!)^2] (* _Harvey P. Dale_, Apr 19 2015 *)

%o (PARI) { a=0; for (n=0, 100, write("b061062.txt", n, " ", a+=(n!)^2) ) } \\ _Harry J. Smith_, Jul 17 2009

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

%K nonn

%O 0,2

%A _Jason Earls_, May 27 2001

%E More terms from _T. D. Noe_, Dec 08 2004