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

0,4

Links

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

Mathematica

seq[n_] := InverseSeries[x/(1 + Sum[If[PrimeQ[k], k*2^(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 *)

Prog

(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)}

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