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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 (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^(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

(Sage)

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: A277710 A286148 A194048 * A104634 A194008 A060422

Adjacent sequences: A158865 A158866 A158867 * A158869 A158870 A158871

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 28 2009

EXTENSIONS

Edited by G. C. Greubel, Mar 07 2022

STATUS

approved

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Last modified December 6 12:58 EST 2022. Contains 358634 sequences. (Running on oeis4.)