A264028 Triangle read by rows: T(n, k) = Sum_{t=k..n-3} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-3,t).

6, 18, 6, 78, 36, 6, 426, 234, 54, 6, 2790, 1704, 468, 72, 6, 21234, 13950, 4260, 780, 90, 6, 183822, 127404, 41850, 8520, 1170, 108, 6, 1781802, 1286754, 445914, 97650, 14910, 1638, 126, 6, 19104774, 14254416, 5147016, 1189104, 195300, 23856, 2184, 144, 6

Offset

3,1

Links

Table of n, a(n) for n=3..47.

J. Liese, J. Remmel, Q-analogues of the number of permutations with k-excedances, PU. M. A. Vol. 21 (2010), No. 2, pp. 285-320 (see E_{n,3}(x) in Table 1 p. 291).

Example

Triangle begins:
6;
18, 6;
78, 36, 6;
426, 234, 54, 6;
2790, 1704, 468, 72, 6;

Mathematica

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 *)

Prog

(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(); ); }

Crossrefs

Cf. A008290, A123513.

Sequence in context: A077022 A074923 A093061 * A078741 A248461 A129870

Adjacent sequences: A264025 A264026 A264027 * A264029 A264030 A264031

Keyword

nonn,tabl

Author

Michel Marcus, Nov 01 2015

Status

approved