A113245 a(n) = floor(binomial(2n,2k)/binomial(n,k)).

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 11, 7, 1, 1, 9, 21, 21, 9, 1, 1, 11, 33, 46, 33, 11, 1, 1, 13, 47, 85, 85, 47, 13, 1, 1, 15, 65, 143, 183, 143, 65, 15, 1, 1, 17, 85, 221, 347, 347, 221, 85, 17, 1, 1, 19, 107, 323, 599, 733, 599, 323, 107, 19, 1, 1, 21, 133, 452, 969, 1399

Offset

0,5

Comments

Row sums of inverse appear to be A000007.

Links

Table of n, a(n) for n=0..71.

Formula

Number triangle T(n, k)=if(k<=n, floor(C(2n, 2k)/C(n, k)), 0).

Example

Triangle begins
1;
1, 1;
1, 3, 1;
1, 5, 5, 1;
1, 7, 11, 7, 1;
1, 9, 21, 21, 9, 1;
1, 11, 33, 46, 33, 11, 1;

Mathematica

Flatten[ Table[ Floor[ Binomial[2n, 2k]/Binomial[n, k]], {n, 0, 11}, {k, 0, n}]] (* Robert G. Wilson v, Oct 21 2005 *)

Crossrefs

Even terms are in A111304.

Sequence in context: A026615 A026681 A109128 * A103450 A128254 A277930

Adjacent sequences: A113242 A113243 A113244 * A113246 A113247 A113248

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 20 2005

Status

approved