A192658 Binomial convolution of the Floor-Sqrt transform of central binomial coefficients.

1, 2, 6, 20, 72, 270, 1040, 4036, 15714, 61226, 238778, 930716, 3628520, 14143922, 55134174, 214941488, 838158510, 3269630046, 12761106790, 49834920864, 194743761948, 761543265544, 2980128724806, 11670402459630, 45734346816026, 179348093549914, 703781965002650

Offset: 0

Author

Emanuele Munarini, Jul 07 2011

Keywords

• nonn

Crossrefs

Cf. A000984, A192655.

Programs

Mathematica

Table[Sum[Binomial[n,k]Floor[Sqrt[Binomial[2k,k]]]Floor[Sqrt[Binomial[2n-2k,n-k]]],{k,0,n}],{n,0,100}]

Maxima

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * floor(sqrt(binomial(2*k,k))) * floor(sqrt(binomial(2*n-2*k,n-k))).