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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 01 2018
STATUS
approved