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

1,3

Comments

See A339301 for additional details.

Links

Table of n, a(n) for n=1..19.

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.

Prog

(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)))}

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.

Sequence in context: A195229 A366654 A367488 * A296389 A077290 A222780

Adjacent sequences: A339297 A339298 A339299 * A339301 A339302 A339303

Keyword

nonn

Author

Andrew Howroyd, Dec 22 2020

Status

approved