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Convolution of the Floor-Sqrt transform of central binomial coefficients.
1

%I #7 Nov 16 2021 21:33:24

%S 1,2,5,12,28,62,138,300,646,1378,2919,6148,12890,26914,56010,116224,

%T 240567,496854,1024202,2107660,4330651,8886094,18210883,37278902,

%U 76234264,155750644,317932560,648477346,1321706751,2692024172,5479576436,11146993980,22663554750,46054591760

%N Convolution of the Floor-Sqrt transform of central binomial coefficients.

%H Vincenzo Librandi, <a href="/A192657/b192657.txt">Table of n, a(n) for n = 0..87</a>

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

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

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

%K nonn

%O 0,2

%A _Emanuele Munarini_, Jul 07 2011