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A303874
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Number of noncrossing partitions of an n-set up to rotation with all blocks having a prime number of elements.
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2
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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
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OFFSET
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0,6
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COMMENTS
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The number of such noncrossing partitions counted distinctly is given by A210737.
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LINKS
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PROG
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(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))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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