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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 Table of n, a(n) for n=0..54. 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 Cf. A021012, A196347, A002894. Row sums are A253665. Sequence in context: A205839 A138024 A167656 * A174298 A196347 A021012 Adjacent sequences: A253663 A253664 A253665 * A253667 A253668 A253669 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.)