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A297899 Triangle read by rows, T(n, k) = binomial(n, k)*hypergeom([k-n, n+1], [k+2], -4), for n >= 0 and 0 <= k <= n. 0
1, 5, 1, 45, 10, 1, 505, 115, 15, 1, 6345, 1460, 210, 20, 1, 85405, 19765, 2990, 330, 25, 1, 1204245, 279710, 43635, 5220, 475, 30, 1, 17558705, 4088615, 651165, 81955, 8275, 645, 35, 1, 262577745, 61254760, 9901860, 1290520, 139350, 12280, 840, 40, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

EXAMPLE

Triangle starts:

[0]       1

[1]       5,      1

[2]      45,     10,     1

[3]     505,    115,    15,    1

[4]    6345,   1460,   210,   20,   1

[5]   85405,  19765,  2990,  330,  25,  1

[6] 1204245, 279710, 43635, 5220, 475, 30, 1

MATHEMATICA

T[n_, k_] := Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -4];

Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

CROSSREFS

T(n, 0) = A133305(n). Row sums are A297705, alternating row sums are A131765.

Cf. A103209.

Sequence in context: A134275 A264774 A114154 * A134273 A048897 A049029

Adjacent sequences:  A297896 A297897 A297898 * A297900 A297901 A297902

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jan 08 2018

STATUS

approved

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Last modified February 21 19:40 EST 2019. Contains 320376 sequences. (Running on oeis4.)