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A253666 Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
T(n,k) = C(n,k)*A056040(k).
T(2*n,n) = C(2*n,n)^2.
EXAMPLE
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.
MAPLE
T := (n, k) -> n!*binomial(n, k)/(iquo(n, 2)!)^2:
seq(print(seq(T(n, k), k=0..n)), n=0..9);
PROG
(Magma) [Binomial(n, k)*Factorial(n)/Factorial(Floor(n/2))^2: k in [0..n], n in [0..10]]; // Bruno Berselli, Feb 02 2015
CROSSREFS
Row sums are A253665.
Sequence in context: A205839 A138024 A167656 * A174298 A196347 A021012
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Feb 01 2015
STATUS
approved

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Last modified May 30 15:08 EDT 2024. Contains 372968 sequences. (Running on oeis4.)