A339230 Number of oriented series-parallel networks with integer valued elements summing to n.

1, 3, 9, 32, 120, 490, 2077, 9158, 41401, 191232, 897849, 4273794, 20573696, 99994830, 490000756, 2418246995, 12008813611, 59962351145, 300864703306, 1516196518032, 7670827035223, 38946578808655, 198379559337073, 1013452414823740, 5191372465942866, 26658747310696437

Offset

1,2

Comments

See A339228 for additional details.

Links

Table of n, a(n) for n=1..26.

Example

In the following examples elements in series are juxtaposed and elements in parallel are separated by '|'.
a(1) = 1: (1).
a(2) = 3: (2), (11), (1|1).
a(3) = 9: (3), (12), (21), (1(1|1)), ((1|1)1), (111), (1|2), (1|11), (1|1|1).

Prog

(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
EdgeWeightedT(u)={my(Z=x*Ser(u)); my(p=Z+O(x^2)); for(n=2, #u, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); Vec(p)}
seq(n)={EdgeWeightedT(vector(n, i, 1))}

Crossrefs

Cf. A339228, A339229.

Sequence in context: A091841 A063020 A104184 * A193621 A344623 A320180

Adjacent sequences: A339227 A339228 A339229 * A339231 A339232 A339233

Keyword

nonn

Author

Andrew Howroyd, Nov 29 2020

Status

approved