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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.)