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A320904
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T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.
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0
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1, 1, 3, 1, 5, 7, 1, 7, 16, 15, 1, 9, 29, 42, 31, 1, 11, 46, 93, 99, 63, 1, 13, 67, 176, 256, 219, 127, 1, 15, 92, 299, 562, 638, 466, 255, 1, 17, 121, 470, 1093, 1586, 1486, 968, 511, 1, 19, 154, 697, 1941, 3473, 4096, 3302, 1981, 1023
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..54.
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EXAMPLE
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Triangle starts:
[0] 1
[1] 1, 3
[2] 1, 5, 7
[3] 1, 7, 16, 15
[4] 1, 9, 29, 42, 31
[5] 1, 11, 46, 93, 99, 63
[6] 1, 13, 67, 176, 256, 219, 127
[7] 1, 15, 92, 299, 562, 638, 466, 255
[8] 1, 17, 121, 470, 1093, 1586, 1486, 968, 511
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MAPLE
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T := (n, k) -> binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n-k+1)], -1):
for n from 0 to 11 do seq(simplify(T(n, k)), k = 0..n) od;
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CROSSREFS
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Row sums are A105693(n-1).
Cf. A097750.
Sequence in context: A221881 A201811 A199898 * A193844 A201552 A216182
Adjacent sequences: A320901 A320902 A320903 * A320905 A320906 A320907
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny, Oct 28 2018
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STATUS
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approved
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