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A339300
Number of essentially parallel oriented series-parallel networks with n labeled elements and without multiple unit elements in parallel.
2
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.
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 22 2020
STATUS
approved