A339299 Number of essentially series oriented series-parallel networks with n labeled elements and without multiple unit elements in parallel.

0, 2, 6, 72, 840, 14040, 276360, 6494880, 175452480, 5375311200, 183962227680, 6958070380800, 288200792880000, 12974113884251520, 630742839699772800, 32933429270386444800, 1838083950894102912000, 109201772719684867622400, 6880730833827011402841600

Offset: 1

Author

Andrew Howroyd, Dec 22 2020

Keywords

• nonn

Comments

See A339301 for additional details.

Crossrefs

A058349 is the case with multiple unit elements in parallel allowed.

A058380 is the case that order is not significant in series configurations.

Cf. A339288 (unlabeled), A339300, 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(p-p/(1+p)), -n)}

Formula

E.g.f.: P(x)^2/(1 - P(x)) where P(x) is the e.g.f. of A339300.

E.g.f.: B(x)^2/(1 + B(x)) where B(x) is the e.g.f. of A339301.

E.g.f.: B(log(1+x)) where x + B(x) is the e.g.f. of A058349.