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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.

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

CROSSREFS

T(n, 0) = A001850(n).

Row sums are A050146(n+1).

Sequence in context: A134768 A295827 A277197 * A322384 A113139 A266577

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 October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)