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A303874 Number of noncrossing partitions of an n-set up to rotation with all blocks having a prime number of elements. 2
1, 0, 1, 1, 1, 2, 3, 5, 8, 17, 37, 71, 179, 366, 919, 2069, 5027, 12053, 29098, 71846, 175485, 437438, 1087122, 2723326, 6860525, 17301606, 43957596, 111748571, 285591775, 731432424, 1879009622, 4841510973, 12500324496, 32366232373, 83962263464, 218309244314 (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

NCPartitionsModCyclic(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);

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)));

T + 2 + intformal(sum(d=1, n, eulerphi(d)*varpow(q, d))/x) - p

}

Vec(NCPartitionsModCyclic(vector(40, k, isprime(k))))

CROSSREFS

Cf. A054357 (unrestricted), A175954 (1 or 2), A210737, A295198, A303875.

Sequence in context: A108054 A123612 A077177 * A145793 A113879 A205303

Adjacent sequences:  A303871 A303872 A303873 * A303875 A303876 A303877

KEYWORD

nonn

AUTHOR

Andrew Howroyd, May 01 2018

STATUS

approved

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)