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%I #21 Feb 14 2021 18:33:34
%S 1,3,53,106,427,3416,6806,13665,27330,130030,220227,437666
%N Numbers k such that Sum_{j=1..k-1} (2*j)!/4^j is an integer.
%C Next term > 1900000.
%t seq={}; sum=0; fak=1; k=0; While[k<10000, sum+=fak; If[Denominator[sum]==1, AppendTo[seq,k+1]]; k++; fak*=k*(2k-1)/2;]; seq
%Y Cf. A215972, A216043, A216044, A216045.
%K nonn,more
%O 1,2
%A _Vaclav Kotesovec_, Aug 30 2012