A106187 Sequence array for central binomial numbers A000984.

1, 2, 1, 6, 2, 1, 20, 6, 2, 1, 70, 20, 6, 2, 1, 252, 70, 20, 6, 2, 1, 924, 252, 70, 20, 6, 2, 1, 3432, 924, 252, 70, 20, 6, 2, 1, 12870, 3432, 924, 252, 70, 20, 6, 2, 1, 48620, 12870, 3432, 924, 252, 70, 20, 6, 2, 1, 184756, 48620, 12870, 3432, 924, 252, 70, 20, 6, 2, 1

Offset: 0

Author

Paul Barry, Apr 24 2005

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
    1;
    2,  1;
    6,  2, 1;
   20,  6, 2, 1;
   70, 20, 6, 2, 1;
  252, 70, 20, 6, 2, 1;
  ...
The matrix inverse starts:
   1;
  -2,1;
  -2,-2,1;
  -4,-2,-2,1;
  -10,-4,-2,-2,1;
  -28,-10,-4,-2,-2,1;
  -84,-28,-10,-4,-2,-2,1;
  -264,-84,-28,-10,-4,-2,-2,1;
apparently related to A002420. - _R. J. Mathar_, Apr 08 2013
		

Crossrefs

Row sums are A006134.

Antidiagonal sums are A106188.

Cf. A000984.

Programs

Maple

A106187 := proc(n,k)
    binomial(2*(n-k),n-k) ;
end proc: # R. J. Mathar, Apr 08 2013

Mathematica

T[n_, k_] := (((2*n - 2*k)!)/((n - k)!)^2); Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Detlef Meya, Aug 11 2024 *)

Formula

T(n, k) = binomial(2*(n-k), n-k).

Riordan array (1/sqrt(1-4x), x).