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A075837
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Triangle T(n,k) = f(n,k,n-2), n >= 0, 0 <= k <= n, where f is given below.
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4
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1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 12, 14, 12, 1, 1, 30, 45, 45, 30, 1, 1, 60, 114, 138, 114, 60, 1, 1, 105, 245, 357, 357, 245, 105, 1, 1, 168, 468, 808, 960, 808, 468, 168, 1, 1, 252, 819, 1647, 2286, 2286, 1647, 819, 252, 1, 1, 360, 1340, 3090, 4935, 5740, 4935, 3090, 1340, 360, 1, 1, 495, 2079, 5423, 9834, 13090, 13090, 9834, 5423
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OFFSET
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1,8
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LINKS
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FORMULA
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f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).
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EXAMPLE
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1; 1,1; 1,0,1; 1,3,3,1; ...
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MAPLE
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f := proc(n, p, k) convert( binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1), `StandardFunctions`); end;
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MATHEMATICA
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f[n_, p_, k_] := Binomial[n, k]*HypergeometricPFQ[{1 - k, -p, p-n}, {1-n, 1}, 1]; t[n_, n_] = t[_, 0] = 1; t[n_, k_] := f[n, k, n-2]; Table[t[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 17 2014 *)
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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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