%I #9 Aug 22 2018 10:34:23
%S 1,1,1,1,-5,27,-277,895,-27655,248185,-5052519,28731489,-1444496477,
%T 19885473347,-595129566605,4808968469791,-333894246376015,
%U 6195249562217393,-244725707175834895,2563206341379247681,-227039228335442728053,5299214394077195384747,-260053313429315175721413
%N Numerators 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 Numerators of coefficients in expansion of e.g.f. sqrt(1 + Sum_{k>=1} prime(k)*x^k/k!).
%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 Numerator[nmax = 22; 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, A300622 (denominators).
%K sign,frac
%O 0,5
%A _Ilya Gutkovskiy_, Aug 14 2018