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URL: https://oeis.org/A158868

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A158868
Triangle T(n, k) = (2*n+1)!! * 2^(floor((n-1)/2) + floor(k/2) + 1) * Beta(floor(n/2) + floor((k-1)/2) + 2, floor((n-1)/2) + floor(k/2) + 2), read by rows.
2
1, 5, 2, 14, 7, 6, 126, 54, 54, 24, 594, 297, 264, 132, 120, 7722, 3432, 3432, 1560, 1560, 720, 51480, 25740, 23400, 11700, 10800, 5400, 5040, 875160, 397800, 397800, 183600, 183600, 85680, 85680, 40320, 7558200, 3779100, 3488400, 1744200, 1627920, 813960, 766080, 383040, 362880
OFFSET
1,2
FORMULA
T(n, k) = (2*n+1)!! * 2^(floor((n-1)/2) + floor(k/2) + 1) * Beta(floor(n/2) + floor((k-1)/2) + 2, floor((n-1)/2) + floor(k/2) + 2).
T(n, n) = n!. - G. C. Greubel, Mar 07 2022
EXAMPLE
Triangle begins as:
1;
5, 2;
14, 7, 6;
126, 54, 54, 24;
594, 297, 264, 132, 120;
7722, 3432, 3432, 1560, 1560, 720;
51480, 25740, 23400, 11700, 10800, 5400, 5040;
875160, 397800, 397800, 183600, 183600, 85680, 85680, 40320;
7558200, 3779100, 3488400, 1744200, 1627920, 813960, 766080, 383040, 362880;
MATHEMATICA
T[n_, k_]:= (2*n+1)!!*2^(1+Floor[n/2] +Floor[(k-1)/2])*Beta[Floor[n/2] +Floor[(k- 1)/2] +2, Floor[(n-1)/2] +Floor[k/2] +2];
Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Mar 07 2022 *)
PROG
(SageMath)
def T(n, k): return (2*n+1).multifactorial(2)*2^(1+(n//2)+((k-1)//2))*beta(2+(n//2)+((k-1)//2), 2+((n-1)//2)+(k//2))
flatten([[T(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Mar 07 2022
CROSSREFS
Cf. A158867.
Sequence in context: A286148 A369369 A194048 * A104634 A194008 A060422
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 28 2009
EXTENSIONS
Edited by G. C. Greubel, Mar 07 2022
STATUS
approved