A303875 Number of noncrossing partitions of an n-set up to rotation and reflection with all blocks having a prime number of elements.
1, 0, 1, 1, 1, 2, 3, 5, 7, 14, 26, 49, 107, 215, 502, 1112, 2619, 6220, 14807, 36396, 88397, 219920, 545196, 1364669, 3434436, 8658463, 21989434, 55893852, 142823174, 365766327, 939575265, 2420885031, 6250344302, 16183450744, 41981605437, 109155492638
Offset: 0
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..500
Programs
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PARI
\\ number of partitions with restricted block sizes NCPartitionsModDihedral(v)={ my(n=#v); my(p=serreverse( x/(1 + sum(k=1, #v, x^k*v[k])) + O(x^2*x^n) )/x); my(vars=variables(p)); my(varpow(r,d)=substvec(r + O(x^(n\d+1)), vars, apply(t->t^d, vars))); my(q=x*deriv(p)/p, h=varpow(p,2)); my(R=sum(i=0, (#v-1)\2, v[2*i+1]*x*(x^2*h)^i), Q=sum(i=1, #v\2, v[2*i]*(x^2*h)^i), 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))); (T + 2 + intformal(sum(d=1, n, eulerphi(d)*varpow(q,d))/x) - p + (1 + Q + (1+R)^2*h/(1-Q))/2)/2 + O(x*x^n) } Vec(NCPartitionsModDihedral(vector(40,k,isprime(k))))
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