A271706 Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j-1,-n-1)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.

1, -1, 1, 1, 0, 1, -1, 3, 3, 1, 1, 8, 18, 8, 1, -1, 45, 110, 70, 15, 1, 1, 264, 795, 640, 195, 24, 1, -1, 1855, 6489, 6335, 2485, 441, 35, 1, 1, 14832, 59332, 67984, 32550, 7504, 868, 48, 1, -1, 133497, 600732, 789852, 445914, 126126, 19068, 1548, 63, 1

Offset

0,8

Links

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

Example

Triangle starts:
[1]
[-1, 1]
[1, 0, 1]
[-1, 3, 3, 1]
[1, 8, 18, 8, 1]
[-1, 45, 110, 70, 15, 1]
[1, 264, 795, 640, 195, 24, 1]
[-1, 1855, 6489, 6335, 2485, 441, 35, 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-1, -n-1), j=0..n):
seq(seq(T(n, k), k=0..n), n=0..9);

Crossrefs

A052845 (row sums), A000240 (col. 1), A000274 (col. 2), A067998 (diag n,n-1).

Cf. A271703.

Sequence in context: A213660 A099037 A340934 * A172108 A220666 A104378

Adjacent sequences: A271703 A271704 A271705 * A271707 A271708 A271709

Keyword

sign,tabl

Author

Peter Luschny, Apr 20 2016

Status

approved