A213168 a(n) = n!/2 - (n-1)! - n + 2.

0, 0, 4, 33, 236, 1795, 15114, 141113, 1451512, 16329591, 199583990, 2634508789, 37362124788, 566658892787, 9153720575986, 156920924159985, 2845499424767984, 54420176498687983, 1094805903679487982, 23112569077678079981, 510909421717094399980

Offset: 2

Author

Olivier Gérard, Nov 02 2012

Keywords

• nonn
• easy

Comments

Row sums of A142706 for k=1..n-1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A001286.

Cf. A142706, A051683, A152883.

Cf. A200748 (considered as a triangular array).

Programs

Magma

[Factorial(n)/2-Factorial(n-1)-n+2: n in [2..25]]; // Vincenzo Librandi, Sep 09 2016

Maple

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

Mathematica

Table[n!/2 - (n - 1)! - n + 2, {n, 2, 20}]

Maxima

A213168(n):=n!/2-(n-1)!-n+2$
makelist(A213168(n),n,2,30); /* Martin Ettl, Nov 03 2012 */

Formula

a(n) = A001286(n-1) - n + 2. - Anton Zakharov, Sep 08 2016

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

E.g.f.: 1/(2-2*x)+log(1-x)+(2-x)*exp(x). - Alois P. Heinz, Aug 25 2021