OFFSET
1,5
COMMENTS
See A339293 for additional details.
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(2) = 1: (oo).
a(3) = 1: (ooo).
a(4) = 1: (oooo).
a(5) = 2: (ooooo), (o(o|oo)o).
a(6) = 4: (oooooo), ((o|oo)(o|oo)), (o(o|ooo)o), (o(oo|oo)o).
PROG
(PARI) \\ here B(n) gives A339290 as a power series.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
B(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) ))); p}
seq(n, Z=x)={my(q=subst(B((n+1)\2, Z), x, x^2), s=q^2/(1+q), p=O(x^2)); forstep(n=2, n, 2, p=q*(1 + Z + (1 + Z)*x*Ser(EulerT(Vec(p+(s-subst(p, x, x^2))/2, 1-n))) - p)); Vec(p+O(x*x^n), -n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 07 2020
STATUS
approved