

A303729


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


4



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
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OFFSET

0,4


LINKS

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


MATHEMATICA

seq[n_] := InverseSeries[x/(1 + Sum[If[PrimeQ[k], k*2^(k3)*x^k, 0], {k, 2, n}]) + O[x]^(n+2), x]/x;
CoefficientList[seq[28], x] (* JeanFrançois Alcover, May 15 2018, translated from PARI *)


PROG

(PARI) seq(n)={Vec(serreverse(x/(1 + sum(k=2, n, if(isprime(k), k*2^(k3)*x^k))) + O(x^(n+2)) )/x)}


CROSSREFS

Cf. A303730, A303731, A303732.
Sequence in context: A154332 A252595 A292158 * A296544 A136635 A062743
Adjacent sequences: A303726 A303727 A303728 * A303730 A303731 A303732


KEYWORD

nonn


AUTHOR

Andrew Howroyd, Apr 29 2018


STATUS

approved



