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a(n) = n! - n(n-1)/2.
1

%I #9 Feb 18 2019 04:09:21

%S 1,1,1,3,18,110,705,5019,40292,362844,3628755,39916745,479001534,

%T 6227020722,87178291109,1307674367895,20922789887880,355687428095864,

%U 6402373705727847,121645100408831829,2432902008176639810,51090942171709439790,1124000727777607679769

%N a(n) = n! - n(n-1)/2.

%C Largest term in the factor partition of A114310(n).

%e a(6) = 705*A114310(6) = 84600 = 1*2*3*4*5*705.

%p a:=n->sum((n!)-j, j=0..n):a(-1):=1: seq(a(n), n=-1..21); # _Zerinvary Lajos_, May 26 2008

%t Table[n!-n(n-1)/2,{n,0,30}] (* _Harvey P. Dale_, Aug 27 2013 *)

%Y Cf. A114310.

%K nonn

%O 0,4

%A _Amarnath Murthy_, Nov 26 2005