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%I #8 Nov 22 2015 21:58:31
%S 2,4,2,14,8,2,64,42,12,2,362,256,84,16,2,2428,1810,640,140,20,2,18806,
%T 14568,5430,1280,210,24,2,165016,131642,50988,12670,2240,294,28,2,
%U 1616786,1320128,526568,135968,25340,3584,392,32,2,17487988,14551074,5940576,1579704,305928,45612,5376,504,36,2
%N Triangle read by rows: T(n, k) = Sum_{t=k..n-2} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-2,t).
%H J. Liese, J. Remmel, <a href="http://puma.dimai.unifi.it/21_2/10_Liese_Remmel.pdf">Q-analogues of the number of permutations with k-excedances</a>, PU. M. A. Vol. 21 (2010), No. 2, pp. 285-320 (see E_{n,2}(x) in Table 1 p. 291).
%e Triangle begins:
%e 2;
%e 4, 2;
%e 14, 8, 2;
%e 64, 42, 12, 2;
%e 362, 256, 84, 16, 2;
%e ...
%t Table[Sum[(-1)^(t - k) (n - t)!*Binomial[t, k] Binomial[n - 2, t], {t, k, n - 2}], {n, 2, 11}, {k, 0, n - 2}] // Flatten (* _Michael De Vlieger_, Nov 01 2015 *)
%o (PARI) tabl(nn) = {for (n=2, nn, for (k=0, n-2, print1(sum(t=k, n-2, (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-2,t)), ", ");); print(););}
%Y Cf. A008290, A123513.
%K nonn,tabl
%O 2,1
%A _Michel Marcus_, Nov 01 2015
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