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%I #12 May 15 2018 08:35:19
%S 1,0,1,3,2,35,32,315,746,2304,12422,27621,150729,465387,1762427,
%T 7239244,23799382,102216580,360900542,1416054762,5522838696,
%U 20534319262,82389314900,311135342409,1223933415631,4773363130810,18490946264039,73109087367264,284357219601461
%N Number of noncrossing path sets on n nodes with each path having a prime number of nodes.
%H Andrew Howroyd, <a href="/A303729/b303729.txt">Table of n, a(n) for n = 0..500</a>
%t seq[n_] := InverseSeries[x/(1 + Sum[If[PrimeQ[k], k*2^(k-3)*x^k, 0], {k, 2, n}]) + O[x]^(n+2), x]/x;
%t CoefficientList[seq[28], x] (* _Jean-François Alcover_, May 15 2018, translated from PARI *)
%o (PARI) seq(n)={Vec(serreverse(x/(1 + sum(k=2, n, if(isprime(k), k*2^(k-3)*x^k))) + O(x^(n+2)) )/x)}
%Y Cf. A303730, A303731, A303732.
%K nonn
%O 0,4
%A _Andrew Howroyd_, Apr 29 2018
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