OFFSET
0,5
LINKS
Bernhard Gittenberger, Emma Yu Jin, Michael Wallner, On the shape of random Pólya structures, arXiv|1707.02144 [math.CO], 2017; Discrete Math., 341 (2018), 896-911.
EXAMPLE
1, 0, 1/2, 1/3, 7/8, 11/30, 281/144, 449/840, ...
MATHEMATICA
TreeGf[nn_] := Module[{A}, A = Table[1, nn]; For[n = 1, n <= nn-1, n++, A[[n+1]] = 1/n Sum[Sum[d A[[d]], {d, Divisors[k]}] A[[n-k+1]], {k, 1, n}] ]; A];
fracts[nn_] := Module[{v, t}, v = Table[0, nn+1]; t = TreeGf[nn]; v[[1]]=1; For[n=2, n <= nn, n++, v[[n+1]] = Sum[v[[n-i+1]] Sum[If[d != i, d t[[d]], 0], {d, Divisors[i]}], {i, 2, n}]/n]; v];
fracts[22] // Numerator (* Jean-François Alcover, Aug 05 2018, after Andrew Howroyd *)
PROG
(PARI) \\ See reference for recursion; TreeGf is gf of A000081.
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
fracts(n)={my(v=vector(n+1), t=Vec(TreeGf(n))); v[1]=1; for(n=2, n, v[n+1]=sum(i=2, n, v[n-i+1]*sumdiv(i, d, if(d<>i, d*t[d])))/n); v}
seq(n)={apply(f->numerator(f), fracts(n))} \\ Andrew Howroyd, Jun 21 2018
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Apr 02 2018
EXTENSIONS
a(8)-a(22) from Andrew Howroyd, Jun 21 2018
STATUS
approved