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A253666
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Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.
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2
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1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 6, 24, 36, 24, 6, 30, 150, 300, 300, 150, 30, 20, 120, 300, 400, 300, 120, 20, 140, 980, 2940, 4900, 4900, 2940, 980, 140, 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70, 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630
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OFFSET
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0,4
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LINKS
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FORMULA
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T(2*n,n) = C(2*n,n)^2.
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EXAMPLE
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Triangle begins:
. 1;
. 1, 1;
. 2, 4, 2;
. 6, 18, 18, 6;
. 6, 24, 36, 24, 6;
. 30, 150, 300, 300, 150, 30;
. 20, 120, 300, 400, 300, 120, 20;
. 140, 980, 2940, 4900, 4900, 2940, 980, 140;
. 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70;
. 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630; etc.
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MAPLE
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T := (n, k) -> n!*binomial(n, k)/(iquo(n, 2)!)^2:
seq(print(seq(T(n, k), k=0..n)), n=0..9);
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PROG
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(Magma) [Binomial(n, k)*Factorial(n)/Factorial(Floor(n/2))^2: k in [0..n], n in [0..10]]; // Bruno Berselli, Feb 02 2015
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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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