A192633 Partial sums of the Floor-Sqrt transform of Catalan numbers.

1, 2, 3, 5, 8, 14, 25, 45, 82, 151, 280, 522, 978, 1839, 3474, 6587, 12533, 23919, 45773, 87811, 168830, 325246, 627706, 1213418, 2349157, 4554139, 8839854, 17178532, 33418850, 65077059, 126842635, 247443779, 483100446, 943899893, 1845533988, 3610834385, 7069128528, 13847830787

Offset

0,2

Links

Table of n, a(n) for n=0..37.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Partial sums of A186546.

Sequence in context: A345235 A128021 A036241 * A125028 A349777 A119262

Adjacent sequences: A192630 A192631 A192632 * A192634 A192635 A192636

Keyword

nonn

Author

Emanuele Munarini, Jul 07 2011

Status

approved