%I #18 Apr 18 2023 15:59:13
%S 1,7,67,767,9587,126011,1711595,23796515,336666215,4828084575,
%T 69994481871,1023793569567,15086216016367,223704570996367,
%U 3335098322412367,49954148031128767,751296616443141667
%N a(n) = Sum_{k=0..n} binomial(2*k, k) * binomial(2*k+1,k).
%C Old name was "A binomial sum".
%H Vincenzo Librandi, <a href="/A082578/b082578.txt">Table of n, a(n) for n = 0..200</a>
%F Recurrence: (n+3)*(n+2)*a(n+2) - (17*n^2+69*n+66)*a(n+1) + (16*n^2+64*n+60)*a(n) = 0.
%F a(n) ~ 2^(4*n+5)/(15*Pi*n). - _Vaclav Kotesovec_, Oct 14 2012
%t Table[Sum[Binomial[2k,k]*Binomial[2k+1,k],{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 14 2012 *)
%o (Maxima) makelist(sum(binomial(2*k,k)*binomial(2*k+1,k),k,0,n),n,0,12);
%Y Partial sums of A000894.
%K easy,nonn
%O 0,2
%A _Emanuele Munarini_, May 07 2003
%E Name changed by _Wesley Ivan Hurt_, Apr 18 2023