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

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

Mathematica

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

Prog

 (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);

Crossrefs

Sequence in context: A150133 A244783 A216837 * A049141 A049129 A063376

Adjacent sequences: A192655 A192656 A192657 * A192659 A192660 A192661

Keyword

nonn

Author

Emanuele Munarini, Jul 07 2011

Status

approved