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A297898 Triangle read by rows, T(n, k) = (-1)^(n-k)*binomial(n,k)*hypergeom([k - n, n + 1], k + 1, 2), for n >= 0 and 0 <= k <= n. 0
1, 3, 1, 13, 4, 1, 63, 19, 5, 1, 321, 96, 26, 6, 1, 1683, 501, 138, 34, 7, 1, 8989, 2668, 743, 190, 43, 8, 1, 48639, 14407, 4043, 1059, 253, 53, 9, 1, 265729, 78592, 22180, 5908, 1462, 328, 64, 10, 1, 1462563, 432073, 122468, 33028, 8378, 1966, 416, 76, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
T(n, 0) = A001850(n).
Row sums are A050146(n+1).
Sequence in context: A134768 A295827 A277197 * A322384 A360088 A113139
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 08 2018
STATUS
approved

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Last modified April 19 23:15 EDT 2024. Contains 371798 sequences. (Running on oeis4.)