A192653 Binomial convolution of the Floor-Sqrt transform of Catalan numbers.

1, 2, 4, 10, 28, 82, 264, 866, 2984, 10476, 37500, 135916, 496242, 1821384, 6712394, 24818020, 92016874, 342043052, 1274461144, 4759439600, 17812520318, 66803249358, 251038475982, 945202437760, 3565529448118, 13474452634994, 51010511291144, 193438196953970

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)/(k+1)))*floor(sqrt(binomial(2*n-2*k,n-k)/(n-k+1))),k=0..n).

Mathematica

 Table[Sum[Binomial[n, k]Floor[Sqrt[Binomial[2k, k]/(k+1)]]Floor[Sqrt[Binomial[2n-2k, n-k]/(n-k+1)]], {k, 0, n}], {n, 0, 100}]

Prog

 (Maxima) makelist(sum(binomial(n, k)*floor(sqrt(binomial(2*k, k)/(k+1)))*floor(sqrt(binomial(2*n-2*k, n-k)/(n-k+1))), k, 0, n), n, 0, 24);

Crossrefs

Sequence in context: A187256 A148110 A149823 * A149824 A331938 A302146

Adjacent sequences: A192650 A192651 A192652 * A192654 A192655 A192656

Keyword

nonn

Author

Emanuele Munarini, Jul 07 2011

Status

approved