A339300 Number of essentially parallel oriented series-parallel networks with n labeled elements and without multiple unit elements in parallel.

1, 0, 6, 36, 540, 8400, 169680, 3966480, 107518320, 3295283040, 112888369440, 4272403544640, 177061349424960, 7974538914101760, 387840385867334400, 20257533315635616000, 1130954856127948051200, 67208532822729871372800, 4235759061057115720128000

Offset: 1

Author

Andrew Howroyd, Dec 22 2020

Keywords

• nonn

Comments

See A339301 for additional details.

Crossrefs

A048174 is the case with multiple edges in parallel allowed.

A058379 is the case that order is not significant in series configurations.

Cf. A339289 (unlabeled), A339299, A339301.

Programs

PARI

seq(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = (1 + Z)*exp(p^2/(1+p)) - 1); Vec(serlaplace(1-1/(1+p)))}

Formula

E.g.f. (1 + x)*exp(S(x)) - S(x) - 1 where S(x) is the e.g.f. of A339299.

E.g.f.: B(x)/(1 + B(x)) where B(x) is the e.g.f. of A339301.

E.g.f.: B(log(1+x)) where B(x) is the e.g.f. of A048174.