|
|
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.
|
|
0
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|