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%I #6 Sep 26 2023 17:01:53
%S 1,-3,13,-67,379,-2267,14065,-89515,580379,-3815731,25356051,
%T -169898467,1145825123,-7767073859,52858784539,-360823702851,
%U 2468606626813,-16915880702563,116028193869805,-796200367684945,5463239318586601,-37465765826805457,256664142145450777,-1755608165010431139
%N G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k) * A(x)^k.
%C Reversion of g.f. for odd prime numbers together with 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>
%t nmax = 24; A[_] = 0; Do[A[x_] = x - Sum[Prime[k] A[x]^k, {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t nmax = 24; CoefficientList[InverseSeries[Series[x + Sum[Prime[k] x^k, {k, 2, nmax}], {x, 0, nmax}], x], x] // Rest
%Y Cf. A006005, A007296.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Sep 25 2023