A271704 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.

1, 0, 1, 0, 3, 1, 0, 11, 8, 1, 0, 49, 57, 15, 1, 0, 261, 424, 174, 24, 1, 0, 1631, 3425, 1930, 410, 35, 1, 0, 11743, 30336, 21855, 6320, 825, 48, 1, 0, 95901, 294553, 259161, 95235, 16835, 1491, 63, 1, 0, 876809, 3123632, 3251500, 1452976, 325150, 38864, 2492, 80, 1

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Example

Triangle starts:
[1]
[0, 1]
[0, 3,     1]
[0, 11,    8,     1]
[0, 49,    57,    15,    1]
[0, 261,   424,   174,   24,   1]
[0, 1631,  3425,  1930,  410,  35,  1]
[0, 11743, 30336, 21855, 6320, 825, 48, 1]

Maple

L := (n, k) -> `if`(k<0 or k>n, 0, (n-k)!*binomial(n, n-k)*binomial(n-1, n-k)):
T := (n, k) -> add(L(j, k)*binomial(-j, -n)*(-1)^(n-j), j=0..n):
seq(seq(T(n, k), k=0..n), n=0..9);

Crossrefs

A001339 (col. 1), A005563 (diag. n,n-1).

Cf. A271703.

Sequence in context: A245667 A067176 A249480 * A307419 A256892 A256893

Adjacent sequences: A271701 A271702 A271703 * A271705 A271706 A271707

Keyword

nonn,tabl

Author

Peter Luschny, Apr 14 2016

Status

approved