OFFSET
1,4
COMMENTS
See A339290 for additional details.
FORMULA
G.f.: B(x)/(1 + B(x)) where B(x) is the g.f. of A339290.
EXAMPLE
In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
a(1) = 1: (o).
a(3) = 1: (o|oo).
a(4) = 2: (o|ooo), (oo|oo).
a(5) = 5: (o|oooo), (o|o(o|oo)), (o|(o|oo)o), (oo|ooo), (o|oo|oo).
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = Z + (1 + Z)*x*Ser(EulerT( Vec(p^2/(1+p), -n) ))); Vec(1-1/(1+p))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 07 2020
STATUS
approved