A192652 Convolution of the Floor-Sqrt transform of Catalan numbers.

1, 2, 3, 6, 11, 22, 44, 86, 169, 332, 652, 1280, 2513, 4932, 9688, 19040, 37439, 73658, 144985, 285530, 562589, 1108994, 2187050, 4314894, 8516372, 16815264, 33213075, 65624052, 129705457, 256441194, 507160201, 1003284894, 1985269126, 3929390078, 7779228124, 15404540776

Offset

0,2

Links

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

Formula

a(n) = sum(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[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(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: A337090 A331993 A027214 * A132831 A354208 A007477

Adjacent sequences: A192649 A192650 A192651 * A192653 A192654 A192655

Keyword

nonn

Author

Emanuele Munarini, Jul 07 2011

Status

approved