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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened 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 Cf. A158868, A268363. Sequence in context: A329162 A344817 A094414 * A107984 A133178 A154225 Adjacent sequences: A158864 A158865 A158866 * A158868 A158869 A158870 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Mar 28 2009 EXTENSIONS Edited by G. C. Greubel, Mar 08 2022 STATUS approved

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Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)