A335748 T(n,k) = (-1)^n*(binomial(2*k,k)/(k+1))*Sum_{j=0..n} (-1)^j*binomial(k,j)*j^n. Triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.

1, 0, 1, 0, -1, 4, 0, 1, -12, 30, 0, -1, 28, -180, 336, 0, 1, -60, 750, -3360, 5040, 0, -1, 124, -2700, 21840, -75600, 95040, 0, 1, -252, 9030, -117600, 705600, -1995840, 2162160, 0, -1, 508, -28980, 571536, -5292000, 25280640, -60540480, 57657600

Offset

0,6

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = (-1)^n*CatalanNumber(k)*Sum_{j=0..n}(-1)^j*binomial(k, j)*j^n.

Example

                             [0] 1
                           [1] 0, 1
                         [2] 0, -1, 4
                       [3] 0, 1, -12, 30
                   [4] 0, -1, 28, -180, 336
                [5] 0, 1, -60, 750, -3360, 5040
          [6] 0, -1, 124, -2700, 21840, -75600, 95040
   [7] 0, 1, -252, 9030, -117600, 705600, -1995840, 2162160
[8] 0, -1, 508, -28980, 571536, -5292000, 25280640, -60540480, 57657600

Crossrefs

Cf. A006531 (row sums), A052895 (absolute row sums), T(n,n) = A001761(n) (signed A292220(n)).

Sequence in context: A127153 A178979 A228270 * A266488 A189355 A221817

Adjacent sequences: A335745 A335746 A335747 * A335749 A335750 A335751

Keyword

sign,tabl

Author

Peter Luschny, Jul 09 2020

Status

approved