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%I #20 Sep 08 2022 08:46:02
%S 0,0,4,33,236,1795,15114,141113,1451512,16329591,199583990,2634508789,
%T 37362124788,566658892787,9153720575986,156920924159985,
%U 2845499424767984,54420176498687983,1094805903679487982,23112569077678079981,510909421717094399980
%N a(n) = n!/2 - (n-1)! - n + 2.
%C Row sums of A142706 for k=1..n-1.
%H Vincenzo Librandi, <a href="/A213168/b213168.txt">Table of n, a(n) for n = 2..200</a>
%F a(n) = A001286(n-1) - n + 2. - _Anton Zakharov_, Sep 08 2016
%F D-finite with recurrence: 2*(n-3)*a(n) - (2*n^2-6*n+4)*a(n-1)- 2*(n-3)*(n-2)^2 = 0. - _Georg Fischer_, Aug 25 2021
%F E.g.f.: 1/(2-2*x)+log(1-x)+(2-x)*exp(x). - _Alois P. Heinz_, Aug 25 2021
%p f:=gfun:-rectoproc({2*(n-3)*a(n) - (2*n^2-6*n+4)*a(n-1)- 2*(n-3)*(n-2)^2, a(2)=0,a(3)=0},a(n),remember): map(f, [$2..22]); # _Georg Fischer_, Aug 25 2021
%t Table[n!/2 - (n - 1)! - n + 2, {n, 2, 20}]
%o (Maxima) A213168(n):=n!/2-(n-1)!-n+2$
%o makelist(A213168(n),n,2,30); /* _Martin Ettl_, Nov 03 2012 */
%o (Magma) [Factorial(n)/2-Factorial(n-1)-n+2: n in [2..25]]; // _Vincenzo Librandi_, Sep 09 2016
%Y Cf. A001286.
%Y Cf. A142706, A051683, A152883.
%Y Cf. A200748 (considered as a triangular array).
%K nonn,easy
%O 2,3
%A _Olivier Gérard_, Nov 02 2012
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