OFFSET
0,3
LINKS
MAPLE
with(numtheory):
g:= proc(n) option remember; `if`(n=0, 1, add(
mobius(n/d)*binomial(2*d, d), d=divisors(n))/(2*n))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(
d*g(d+1), d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30);
MATHEMATICA
g[n_] := g[n] = If[n == 0, 1, Sum[MoebiusMu[n/d] Binomial[2d, d], {d, Divisors[n]}]/(2n)];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*g[d+1], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 23 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 20 2017
STATUS
approved