cp's OEIS Frontend

A303732 Number of noncrossing path sets on n nodes up to rotation with each path having a prime number of nodes.

%I A303732 #9 May 03 2018 17:02:04
%S A303732 1,0,1,1,1,7,8,45,96,258,1260,2511,12594,35799,126043,482640,1487929,
%T A303732 6012740,20051360,74529198,276148256,977824914,3744986184,13527623583,
%U A303732 50997301218,190934525258,711190503929,2707743977818,10155615925523,38691707792278
%N A303732 Number of noncrossing path sets on n nodes up to rotation with each path having a prime number of nodes.
%H A303732 Andrew Howroyd, <a href="/A303732/b303732.txt">Table of n, a(n) for n = 0..500</a>
%o A303732 (PARI) \\ number of path sets with restricted path lengths
%o A303732 NCPathSetsModCyclic(v)={ my(n=#v);
%o A303732 my(p=serreverse(x/(1 + x*v[1] + sum(k=2, #v, (k*2^(k-3))*x^k*v[k])) + O(x^2*x^n) )/x);
%o A303732 my(vars=variables(p));
%o A303732 my(h=substvec(p + O(x^(n\2+1)),vars,apply(t->t^2, vars)));
%o A303732 my(q=x*deriv(p)/p);
%o A303732 my(Q=sum(i=1, #v\2, v[2*i]*2^(i-1)*(x^2*h)^i));
%o A303732 1 + Q/2 + intformal((p - 1 + sum(d=2, n, eulerphi(d)*substvec(q + O(x^(n\d+1)), vars, apply(t->t^d, vars))))/x)
%o A303732 }
%o A303732 Vec(NCPathSetsModCyclic(vector(30, k, isprime(k))))
%Y A303732 Cf. A303729, A303731.
%K A303732 nonn
%O A303732 0,6
%A A303732 _Andrew Howroyd_, Apr 29 2018