A119829 -id:A119829 - cp's OEIS frontend

A119828 Number triangle T(n,k)=(2n)!/(2k)!.

1, 2, 1, 24, 12, 1, 720, 360, 30, 1, 40320, 20160, 1680, 56, 1, 3628800, 1814400, 151200, 5040, 90, 1, 479001600, 239500800, 19958400, 665280, 11880, 132, 1, 87178291200, 43589145600, 3632428800, 121080960, 2162160, 24024, 182, 1

Offset: 0

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Paul Barry, May 25 2006

easy
nonn
tabl

Row sums are A051396(n+1). Diagonal sums are A119829. Inverse is the bi-diagonal array A119830. E.g.f. cosh(x*y)/(1-y*x^2) produces an aerated version.

			Triangle begins as:
        1,
        2,       1,
       24,      12,      1,
      720,     360,     30,    1,
    40320,   20160,   1680,   56,  1,
  3628800, 1814400, 151200, 5040, 90, 1

Flatten[Table[(2n)!/(2k)!, {n, 0, 7}, {k, 0, n}]] (* James C. McMahon, Sep 23 2024 *)

Number triangle T(n,k)=[k<=n](2n)!/(2k)!

cp's OEIS Frontend

A119828 Number triangle T(n,k)=(2n)!/(2k)!.

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