A264027 Triangle read by rows: T(n, k) = Sum_{t=k..n-2} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-2,t).

2, 4, 2, 14, 8, 2, 64, 42, 12, 2, 362, 256, 84, 16, 2, 2428, 1810, 640, 140, 20, 2, 18806, 14568, 5430, 1280, 210, 24, 2, 165016, 131642, 50988, 12670, 2240, 294, 28, 2, 1616786, 1320128, 526568, 135968, 25340, 3584, 392, 32, 2, 17487988, 14551074, 5940576, 1579704, 305928, 45612, 5376, 504, 36, 2

Offset

2,1

Links

Table of n, a(n) for n=2..56.

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,2}(x) in Table 1 p. 291).

Example

Triangle begins:
2;
4, 2;
14, 8, 2;
64, 42, 12, 2;
362, 256, 84, 16, 2;
...

Mathematica

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 *)

Prog

(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(); ); }

Crossrefs

Cf. A008290, A123513.

Sequence in context: A153801 A354408 A062867 * A113539 A215055 A152877

Adjacent sequences: A264024 A264025 A264026 * A264028 A264029 A264030

Keyword

nonn,tabl

Author

Michel Marcus, Nov 01 2015

Status

approved