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%I #23 Jul 19 2020 11:53:15
%S 1,1,5,23,113,568,2905,15040,78581,413496,2188204,11633666,62089785,
%T 332459890,1785132500,9608402738,51826221461,280063787170,
%U 1515943655628,8217729019538,44606550971500,242419877520384,1318902900434870
%N a(n) = Sum_{i=0..n} binomial(2*i-1,i)*binomial(2*i,n-i).
%H Seiichi Manyama, <a href="/A320326/b320326.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (2*x^3 + 4*x^2 + 2*x)/(sqrt(-4*x^3 - 8*x^2 - 4*x + 1) + 4*x^3 + 8*x^2 + 4*x - 1).
%F Recurrence: n*a(n) = 2*(2*n - 1)*a(n-1) + 8*(n-1)*a(n-2) + 2*(2*n - 3)*a(n-3). - _Vaclav Kotesovec_, Oct 11 2018
%p a:=n->add(binomial(2*i-1,i)*binomial(2*i,n-i),i=0..n): seq(a(n),n=0..25); # _Muniru A Asiru_, Oct 11 2018
%t Table[Sum[Binomial[2*i - 1, i]*Binomial[2*i, n - i], {i, 0, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Oct 11 2018 *)
%o (GAP) List([0..25],n->Sum([0..n],i->Binomial(2*i-1,i)*Binomial(2*i,n-i))); # _Muniru A Asiru_, Oct 11 2018
%o (PARI) a(n) = sum(i=0, n, binomial(2*i-1,i)*binomial(2*i,n-i)); \\ _Michel Marcus_, Oct 11 2018
%Y Cf. A001700.
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Oct 10 2018