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A339299
Number of essentially series oriented series-parallel networks with n labeled elements and without multiple unit elements in parallel.
2
0, 2, 6, 72, 840, 14040, 276360, 6494880, 175452480, 5375311200, 183962227680, 6958070380800, 288200792880000, 12974113884251520, 630742839699772800, 32933429270386444800, 1838083950894102912000, 109201772719684867622400, 6880730833827011402841600
OFFSET
1,2
COMMENTS
See A339301 for additional details.
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.
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(p-p/(1+p)), -n)}
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.
Sequence in context: A295182 A052613 A156493 * A218891 A117515 A265936
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 22 2020
STATUS
approved