A303729 Number of noncrossing path sets on n nodes with each path having a prime number of nodes.

1, 0, 1, 3, 2, 35, 32, 315, 746, 2304, 12422, 27621, 150729, 465387, 1762427, 7239244, 23799382, 102216580, 360900542, 1416054762, 5522838696, 20534319262, 82389314900, 311135342409, 1223933415631, 4773363130810, 18490946264039, 73109087367264, 284357219601461

Offset: 0

Author

Andrew Howroyd, Apr 29 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A303730, A303731, A303732.

Programs

Mathematica

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;
CoefficientList[seq[28], x] (* Jean-François Alcover, May 15 2018, translated from PARI *)

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)}