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%I #15 Jun 27 2018 13:15:03
%S 4,18,104,687,5064,40934,358083,3346832,33123000,345219919,3777134694,
%T 43291666298,518855171115,6491738816768,84656365477452,
%U 1148895613585775,16201725990730392,237030534528945348,3591398122456079285,56254812062478841340,909319044063443870702
%N Expansion of e.g.f. P(P(x)), where P(x) = Sum_{k>=1} prime(k)*x^k/k!.
%C Self-composition of e.g.f. of A000040 (prime numbers).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%e E.g.f.: A(x) = 4*x + 18*x^2/2! + 104*x^3/3! + 687*x^4/4! + 5064*x^5/5! + 40934*x^6/6! + ...
%t p[x_] := p[x] = Sum[Prime[k] x^k/k!, {k, 21}]; a[n_] := a[n] = SeriesCoefficient[p[p[x]], {x, 0, n}]; Table[n! a[n], {n, 21}]
%Y Cf. A000040, A014342, A014345, A030278.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Jun 26 2018
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