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%I #14 Mar 24 2023 10:17:43
%S 1,3,17,23,61,107,421,1103,5777,7563,19801,103681,135721,355323,
%T 1860497,2435423,6376021,11128427,43701901,114413063,599074577,
%U 784198803,2053059121,10749957121,14071876561,36840651123,192900153617
%N a(n) = numerator of Sum_{i=1..n} binomial(2n-i-1,i-1)/i.
%C We conjecture that Sum_{i=1..n} ((1/i)*C(2n-i-1,i-1)) is not an integer for n>1.
%F Sum_{i=1..n} C(2n-i-1,i-1)/i = (2F1(1/2-n,-n;1-2 n;-4) -1)/(2n), where 2F1 is the Gaussian Hypergeometric Function.
%t Table[Numerator[Sum[(1/i)*Binomial[2n-i-1,i-1],{i,1,n}]],{n,1,50}]
%Y Cf. A175386 (denominator).
%K nonn,frac
%O 1,2
%A _Vladimir Shevelev_, _Zak Seidov_, Apr 24 2010
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