cp's OEIS Frontend

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.

%I A158868 #9 Mar 08 2022 03:47:06
%S A158868 1,5,2,14,7,6,126,54,54,24,594,297,264,132,120,7722,3432,3432,1560,
%T A158868 1560,720,51480,25740,23400,11700,10800,5400,5040,875160,397800,
%U A158868 397800,183600,183600,85680,85680,40320,7558200,3779100,3488400,1744200,1627920,813960,766080,383040,362880
%N 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.
%H A158868 G. C. Greubel, <a href="/A158868/b158868.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A158868 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).
%F A158868 T(n, n) = n!. - _G. C. Greubel_, Mar 07 2022
%e A158868 Triangle begins as:
%e A158868         1;
%e A158868         5,       2;
%e A158868        14,       7,       6;
%e A158868       126,      54,      54,      24;
%e A158868       594,     297,     264,     132,     120;
%e A158868      7722,    3432,    3432,    1560,    1560,    720;
%e A158868     51480,   25740,   23400,   11700,   10800,   5400,   5040;
%e A158868    875160,  397800,  397800,  183600,  183600,  85680,  85680,  40320;
%e A158868   7558200, 3779100, 3488400, 1744200, 1627920, 813960, 766080, 383040, 362880;
%t A158868 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];
%t A158868 Table[T[n, k], {n,10}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 07 2022 *)
%o A158868 (Sage)
%o A158868 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))
%o A158868 flatten([[T(n,k) for k in (1..n)] for n in (1..10)]) # _G. C. Greubel_, Mar 07 2022
%Y A158868 Cf. A158867.
%K A158868 nonn,tabl
%O A158868 1,2
%A A158868 _Roger L. Bagula_, Mar 28 2009
%E A158868 Edited by _G. C. Greubel_, Mar 07 2022