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A272099
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Triangle read by rows, T(n,k) = C(n+1,k+1)*F([k-n, k-n-1], [-n-1], -1), where F is the generalized hypergeometric function, for n>=0 and 0<=k<=n.
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0
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1, 4, 1, 12, 5, 1, 32, 18, 6, 1, 80, 56, 25, 7, 1, 192, 160, 88, 33, 8, 1, 448, 432, 280, 129, 42, 9, 1, 1024, 1120, 832, 450, 180, 52, 10, 1, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 5120, 6912, 6400, 4424, 2364, 985, 316, 75, 12, 1
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OFFSET
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0,2
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COMMENTS
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LINKS
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EXAMPLE
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Triangle starts:
1;
4, 1;
12, 5, 1;
32, 18, 6, 1;
80, 56, 25, 7, 1;
192, 160, 88, 33, 8, 1;
448, 432, 280, 129, 42, 9, 1;
1024, 1120, 832, 450, 180, 52, 10, 1;
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MAPLE
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T := (n, k) -> binomial(n+1, k+1)*hypergeom([k-n, k-n-1], [-n-1], -1):
seq(seq(simplify(T(n, k)), k=0..n), n=0..9);
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MATHEMATICA
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T[n_, k_] := Binomial[n+1, k+1] HypergeometricPFQ[{k-n, k-n-1}, {-n-1}, -1];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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