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%I #11 Aug 22 2018 10:34:29
%S 1,1,2,1,4,4,8,4,16,16,32,16,64,64,128,64,256,256,512,256,1024,1024,
%T 2048,1024,4096,4096,8192,4096,16384,16384,32768,16384,65536,65536,
%U 131072,65536,262144,262144,524288,262144,1048576,1048576,2097152,1048576,4194304,4194304,8388608,4194304
%N Denominators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, ... (1 with primes).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Denominators of coefficients in expansion of e.g.f. sqrt(1 + Sum_{k>=1} prime(k)*x^k/k!).
%F Empirical g.f.: (1 + x*(1 + x)^2)/(1 - 4*x^4).
%e 1, 1, 1/2, 1, -5/4, 27/4, -277/8, 895/4, -27655/16, 248185/16, -5052519/32, 28731489/16, -1444496477/64, 19885473347/64, ...
%t Denominator[nmax = 47; CoefficientList[Series[(1 + Sum[Prime[k] x^k/k!, {k, 1, nmax}])^(1/2), {x, 0, nmax}], x] Range[0, nmax] !]
%Y Cf. A008578, A073749, A073750, A300621 (numerators).
%K nonn,frac
%O 0,3
%A _Ilya Gutkovskiy_, Aug 14 2018