cp's OEIS Frontend

A303874 Number of noncrossing partitions of an n-set up to rotation with all blocks having a prime number of elements.

%I A303874 #10 May 03 2018 14:51:51
%S A303874 1,0,1,1,1,2,3,5,8,17,37,71,179,366,919,2069,5027,12053,29098,71846,
%T A303874 175485,437438,1087122,2723326,6860525,17301606,43957596,111748571,
%U A303874 285591775,731432424,1879009622,4841510973,12500324496,32366232373,83962263464,218309244314
%N A303874 Number of noncrossing partitions of an n-set up to rotation with all blocks having a prime number of elements.
%C A303874 The number of such noncrossing partitions counted distinctly is given by A210737.
%H A303874 Andrew Howroyd, <a href="/A303874/b303874.txt">Table of n, a(n) for n = 0..500</a>
%o A303874 (PARI) \\ number of partitions with restricted block sizes
%o A303874 NCPartitionsModCyclic(v)={ my(n=#v);
%o A303874 my(p=serreverse(x/(1 + sum(k=1, #v, x^k*v[k])) + O(x^2*x^n) )/x);
%o A303874 my(vars=variables(p));
%o A303874 my(varpow(r,d)=substvec(r + O(x^(n\d+1)), vars, apply(t->t^d, vars)));
%o A303874 my(q=x*deriv(p)/p);
%o A303874 my(T=sum(k=1, #v, my(t=v[k]); if(t, x^k*t*sumdiv(k, d, eulerphi(d) * varpow(p,d)^(k/d))/k)));
%o A303874 T + 2 + intformal(sum(d=1,n,eulerphi(d)*varpow(q,d))/x) - p
%o A303874 }
%o A303874 Vec(NCPartitionsModCyclic(vector(40, k, isprime(k))))
%Y A303874 Cf. A054357 (unrestricted), A175954 (1 or 2), A210737, A295198, A303875.
%K A303874 nonn
%O A303874 0,6
%A A303874 _Andrew Howroyd_, May 01 2018