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Numerator of the sum of all matrix elements of n X n matrix M[i,j]=CatalanNumber[i]/CatalanNumber[j], where CatalanNumber[k]=(2k)!/k!/(k+1)!=A000108[k].
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%I #4 Jan 29 2013 18:26:18

%S 1,9,68,1364,12064,58303,4517375,1142991,4251679307,138473652271,

%T 240881487689,857560784067,49571162119157,12805922830496929,

%U 167798784068528807,365691567246838709,46160923354240494523

%N Numerator of the sum of all matrix elements of n X n matrix M[i,j]=CatalanNumber[i]/CatalanNumber[j], where CatalanNumber[k]=(2k)!/k!/(k+1)!=A000108[k].

%C p divides a(p-1) for primes p in A007645.

%F a(n) = Numerator[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)),{i,1,n}],{j,1,n}]].

%t Numerator[Table[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)),{i,1,n}],{j,1,n}],{n,1,20}]]

%Y Cf. A000108, A014138, A007645.

%K frac,nonn

%O 1,2

%A _Alexander Adamchuk_, Jul 14 2006