A303839
Number of noncrossing path sets on n nodes up to rotation and reflection with each path having at least two nodes.
Original entry on oeis.org
1, 0, 1, 1, 3, 5, 17, 40, 138, 430, 1546, 5478, 20525, 77310, 298301, 1161692, 4583525, 18239037, 73221198, 296046399, 1205038270, 4933969005, 20311807087, 84029440358, 349201537324, 1457205298510, 6104204225832, 25661191956781, 108231773165825
Offset: 0
Case n=4: There are 3 possibilities:
.
o---o o o o---o
| | /
o---o o---o o---o
.
A303844
Number of noncrossing path sets on n nodes up to rotation with each path having at least two nodes.
Original entry on oeis.org
1, 0, 1, 1, 4, 7, 26, 69, 246, 818, 2976, 10791, 40591, 153959, 594753, 2320696, 9159498, 36467012, 146411208, 592046830, 2409946566, 9867745442, 40623068380, 168058068487, 698400767839, 2914407151002, 12208398647345, 51322369218674, 216463504458521
Offset: 0
Case n=4: There are 4 possibilities:
.
o---o o o o---o o---o
| | / \
o---o o---o o---o o---o
.
A303729
Number of noncrossing path sets on n nodes with each path having a prime number of nodes.
Original entry on oeis.org
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
-
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 *)
-
seq(n)={Vec(serreverse(x/(1 + sum(k=2, n, if(isprime(k), k*2^(k-3)*x^k))) + O(x^(n+2)) )/x)}
Showing 1-3 of 3 results.