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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 Table of n, a(n) for n=0..54. 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 Adjacent sequences: A297895 A297896 A297897 * A297899 A297900 A297901 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.)