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A158867
Triangle T(n, k) = (2*n+1)!! * 2^(1 + floor(n/2) + floor(k/2) + floor((k-1)/2)) * Beta(floor(n/2) + floor((k-1)/2) + 2, floor((n-1)/2) + floor(k/2) + 2), read by rows.
3
1, 5, 4, 14, 14, 12, 126, 108, 108, 96, 594, 594, 528, 528, 480, 7722, 6864, 6864, 6240, 6240, 5760, 51480, 51480, 46800, 46800, 43200, 43200, 40320, 875160, 795600, 795600, 734400, 734400, 685440, 685440, 645120, 7558200, 7558200, 6976800, 6976800, 6511680, 6511680, 6128640, 6128640, 5806080
OFFSET
1,2
FORMULA
T(n, k) = (2*n+1)!! * 2^(1 + floor(n/2) + floor(k/2) + floor((k-1)/2)) * Beta(floor(n/2) + floor((k-1)/2) + 2, floor((n-1)/2) + floor(k/2) + 2).
T(n, n) = A268363(n). - G. C. Greubel, Mar 08 2022
EXAMPLE
Triangle begins as:
1;
5, 4;
14, 14, 12;
126, 108, 108, 96;
594, 594, 528, 528, 480;
7722, 6864, 6864, 6240, 6240, 5760;
51480, 51480, 46800, 46800, 43200, 43200, 40320;
875160, 795600, 795600, 734400, 734400, 685440, 685440, 645120;
7558200, 7558200, 6976800, 6976800, 6511680, 6511680, 6128640, 6128640, 5806080;
MATHEMATICA
T[n_, k_]:= (2*n+1)!!*2^(1+Floor[n/2]+Floor[k/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 08 2022 *)
PROG
(Sage)
def A158867(n, k): return (2*n+1).multifactorial(2)*2^(1+(n//2)+(k//2)+((k-1)//2))*beta(2+(n//2)+((k-1)//2), 2+((n-1)//2)+(k//2))
flatten([[A158867(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Mar 08 2022
CROSSREFS
Sequence in context: A329162 A344817 A094414 * A107984 A133178 A377626
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 28 2009
EXTENSIONS
Edited by G. C. Greubel, Mar 08 2022
STATUS
approved