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%I #8 Nov 22 2015 21:58:44
%S 6,18,6,78,36,6,426,234,54,6,2790,1704,468,72,6,21234,13950,4260,780,
%T 90,6,183822,127404,41850,8520,1170,108,6,1781802,1286754,445914,
%U 97650,14910,1638,126,6,19104774,14254416,5147016,1189104,195300,23856,2184,144,6
%N Triangle read by rows: T(n, k) = Sum_{t=k..n-3} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-3,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,3}(x) in Table 1 p. 291).
%e Triangle begins:
%e 6;
%e 18, 6;
%e 78, 36, 6;
%e 426, 234, 54, 6;
%e 2790, 1704, 468, 72, 6;
%t Table[Sum[(-1)^(t - k) (n - t)!*Binomial[t, k] Binomial[n - 3, t], {t, k, n - 3}], {n, 3, 11}, {k, 0, n - 3}] // Flatten (* _Michael De Vlieger_, Nov 01 2015 *)
%o (PARI) tabl(nn) = {for (n=3, 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 3,1
%A _Michel Marcus_, Nov 01 2015
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