A106187 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..65.

FORMULA

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

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

EXAMPLE

Triangle begins:

2, 1;

6, 2, 1;

20, 6, 2, 1;

70, 20, 6, 2, 1;

252, 70, 20, 6, 2, 1;

...

The matrix inverse starts:

-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

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 *)

CROSSREFS

Row sums are A006134.

Antidiagonal sums are A106188.

Cf. A000984.

Sequence in context: A101024 A124730 A114283 * A110135 A114423 A335109

Adjacent sequences: A106184 A106185 A106186 * A106188 A106189 A106190

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Apr 24 2005

STATUS

approved