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Number of essentially parallel oriented series-parallel networks with n labeled elements and without multiple unit elements in parallel.
2

%I #6 Dec 22 2020 18:26:21

%S 1,0,6,36,540,8400,169680,3966480,107518320,3295283040,112888369440,

%T 4272403544640,177061349424960,7974538914101760,387840385867334400,

%U 20257533315635616000,1130954856127948051200,67208532822729871372800,4235759061057115720128000

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

%C See A339301 for additional details.

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

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

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

%o (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)))}

%Y A048174 is the case with multiple edges in parallel allowed.

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

%Y Cf. A339289 (unlabeled), A339299, A339301.

%K nonn

%O 1,3

%A _Andrew Howroyd_, Dec 22 2020