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A367178
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Triangle read by rows. T(n, k) = binomial(n, k)^2 * CatalanNumber(k).
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0
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1, 1, 1, 1, 4, 2, 1, 9, 18, 5, 1, 16, 72, 80, 14, 1, 25, 200, 500, 350, 42, 1, 36, 450, 2000, 3150, 1512, 132, 1, 49, 882, 6125, 17150, 18522, 6468, 429, 1, 64, 1568, 15680, 68600, 131712, 103488, 27456, 1430, 1, 81, 2592, 35280, 222264, 666792, 931392, 555984, 115830, 4862
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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) = binomial(n, k)^2 * binomial(2*k, k) / (k + 1).
T(n, k) = [x^n] hypergeom([1/2, -n, -n], [1, 2], 4*x).
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EXAMPLE
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Triangle T(n, k) starts:
[0] 1;
[1] 1, 1;
[2] 1, 4, 2;
[3] 1, 9, 18, 5;
[4] 1, 16, 72, 80, 14;
[5] 1, 25, 200, 500, 350, 42;
[6] 1, 36, 450, 2000, 3150, 1512, 132;
[7] 1, 49, 882, 6125, 17150, 18522, 6468, 429;
[8] 1, 64, 1568, 15680, 68600, 131712, 103488, 27456, 1430;
[9] 1, 81, 2592, 35280, 222264, 666792, 931392, 555984, 115830, 4862;
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MAPLE
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T := (n, k) -> binomial(n, k)^2 * binomial(2*k, k) / (k + 1):
seq(seq(T(n, k), k = 0..n), n = 0..9);
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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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