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A320906 T(n, k) = binomial(2*n - k, k - 1)*hypergeom([2, 2, 1 - k], [1, 2*(1 - k + n)], -1), triangle read by rows, T(n,k) for n >= 0 and 0 <= k <= n. 1
0, 0, 1, 0, 1, 6, 0, 1, 8, 24, 0, 1, 10, 39, 80, 0, 1, 12, 58, 150, 240, 0, 1, 14, 81, 256, 501, 672, 0, 1, 16, 108, 406, 955, 1524, 1792, 0, 1, 18, 139, 608, 1686, 3178, 4339, 4608, 0, 1, 20, 174, 870, 2794, 6144, 9740, 11762, 11520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

Triangle starts:

[0] 0

[1] 0, 1

[2] 0, 1,  6

[3] 0, 1,  8,  24

[4] 0, 1, 10,  39,  80

[5] 0, 1, 12,  58, 150,  240

[6] 0, 1, 14,  81, 256,  501,  672

[7] 0, 1, 16, 108, 406,  955, 1524, 1792

[8] 0, 1, 18, 139, 608, 1686, 3178, 4339,  4608

[9] 0, 1, 20, 174, 870, 2794, 6144, 9740, 11762, 11520

MAPLE

T := (n, k) -> binomial(2*n-k, k-1)*hypergeom([2, 2, 1-k], [1, 2*(1-k+n)], -1):

seq(seq(simplify(T(n, k)), k=0..n), n=0..9);

CROSSREFS

Row sums are A320907. T(n, n) = A001788(n).

Cf. A320905.

Sequence in context: A321215 A141108 A019846 * A195445 A215080 A317446

Adjacent sequences:  A320903 A320904 A320905 * A320907 A320908 A320909

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 28 2018

STATUS

approved

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Last modified March 28 05:27 EDT 2020. Contains 333073 sequences. (Running on oeis4.)