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 A303732 Number of noncrossing path sets on n nodes up to rotation with each path having a prime number of nodes. 6

%I

%S 1,0,1,1,1,7,8,45,96,258,1260,2511,12594,35799,126043,482640,1487929,

%T 6012740,20051360,74529198,276148256,977824914,3744986184,13527623583,

%U 50997301218,190934525258,711190503929,2707743977818,10155615925523,38691707792278

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

%H Andrew Howroyd, <a href="/A303732/b303732.txt">Table of n, a(n) for n = 0..500</a>

%o (PARI) \\ number of path sets with restricted path lengths

%o NCPathSetsModCyclic(v)={ my(n=#v);

%o 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 my(vars=variables(p));

%o my(h=substvec(p + O(x^(n\2+1)),vars,apply(t->t^2, vars)));

%o my(q=x*deriv(p)/p);

%o my(Q=sum(i=1, #v\2, v[2*i]*2^(i-1)*(x^2*h)^i));

%o 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 }

%o Vec(NCPathSetsModCyclic(vector(30, k, isprime(k))))

%Y Cf. A303729, A303731.

%K nonn

%O 0,6

%A _Andrew Howroyd_, Apr 29 2018

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Last modified October 20 17:40 EDT 2019. Contains 328268 sequences. (Running on oeis4.)