%I #44 Aug 15 2022 16:49:45

%S 1,5,41,617,15017,533417,25935017,1651637417,133333531817,

%T 13301522971817,1606652445211817,231049185247771817,

%U 39006837228880411817,7639061293780877851817,1717651314017980301851817,439480788011413032845851817,126953027293558583218061851817

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

%H Seiichi Manyama, <a href="/A104344/b104344.txt">Table of n, a(n) for n = 1..253</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FactorialSums.html">Factorial Sums</a>

%F a(n) = A061062(n) - 1. - _Michel Marcus_, Feb 28 2014

%t Table[Sum[(k!)^2,{k,n}],{n,15}] (* _Harvey P. Dale_, Jul 21 2011 *)

%t Accumulate[(Range[20]!)^2] (* Much more efficient than the above program. *) (* _Harvey P. Dale_, Aug 15 2022 *)

%o (PARI) a(n) = sum(k=1, n, k!^2); \\ _Michel Marcus_, Jul 16 2017

%Y Cf. A001044, A061062, A100289.

%Y 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).

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Mar 02 2005

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Sep 24 2009