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A370232
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Triangle read by rows. T(n, k) = binomial(n + k, 2*k)^2.
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1
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1, 1, 1, 1, 9, 1, 1, 36, 25, 1, 1, 100, 225, 49, 1, 1, 225, 1225, 784, 81, 1, 1, 441, 4900, 7056, 2025, 121, 1, 1, 784, 15876, 44100, 27225, 4356, 169, 1, 1, 1296, 44100, 213444, 245025, 81796, 8281, 225, 1, 1, 2025, 108900, 853776, 1656369, 1002001, 207025, 14400, 289, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = [z^k] P(n, z) where P(n, z) = Sum_{k=0..n} binomial(n + k, 2*k) * Pochhammer(n - k + c, 2*k) * z^k / (2*k)! and c = 1.
T(n, k) = [z^k] hypergeom([-n, -n, 1 + n, 1 + n], [1/2, 1/2, 1], z/16).
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EXAMPLE
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Triangle starts:
[0] 1;
[1] 1, 1;
[2] 1, 9, 1;
[3] 1, 36, 25, 1;
[4] 1, 100, 225, 49, 1;
[5] 1, 225, 1225, 784, 81, 1;
[6] 1, 441, 4900, 7056, 2025, 121, 1;
[7] 1, 784, 15876, 44100, 27225, 4356, 169, 1;
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MATHEMATICA
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Table[Binomial[n + k, 2*k]^2, {n, 0, 7}, {k, 0, n}] // Flatten
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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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