OFFSET
0,2
FORMULA
T(n, k) = Sum_{j=0..n - k} binomial(n - k, j)*binomial(n + j, j). - Detlef Meya, Jan 14 2024
EXAMPLE
Triangle starts:
[0] 1
[1] 3, 1
[2] 13, 4, 1
[3] 63, 19, 5, 1
[4] 321, 96, 26, 6, 1
[5] 1683, 501, 138, 34, 7, 1
[6] 8989, 2668, 743, 190, 43, 8, 1
MATHEMATICA
T[n_, k_] := (-1)^(n - k) Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 1, 2];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten
T[n_, k_] := Sum[Binomial[n - k, j]*Binomial[n + j, j], {j, 0, n - k}]; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* Detlef Meya, Jan 14 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 08 2018
STATUS
approved