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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.
0
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
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
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Apr 20 2016
STATUS
approved