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

0,2

Comments

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.

Links

Table of n, a(n) for n=0..35.

Formula

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

Example

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

Mathematica

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

Crossrefs

Sequence in context: A073876 A355587 A276399 * A328826 A297892 A101179

Adjacent sequences: A119825 A119826 A119827 * A119829 A119830 A119831

Keyword

easy,nonn,tabl

Author

Paul Barry, May 25 2006

Status

approved