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A303875 Number of noncrossing partitions of an n-set up to rotation and reflection with all blocks having a prime number of elements. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 29 05:01 EST 2020. Contains 332353 sequences. (Running on oeis4.)