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

0,6

Comments

The number of such noncrossing partitions counted distinctly is given by A210737.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Prog

(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))))

Crossrefs

Cf. A111275, A185100 (1 or 2), A210737, A303874, A303931.

Sequence in context: A028304 A324840 A316475 * A331037 A228652 A157833

Adjacent sequences: A303872 A303873 A303874 * A303876 A303877 A303878

Keyword

nonn

Author

Andrew Howroyd, May 01 2018

Status

approved