

A339152


Number of essentially parallel nonequivalent seriesparallel networks with n elements and without unit elements in parallel.


3



1, 0, 0, 1, 1, 3, 4, 9, 16, 33, 63, 131, 261, 545, 1123, 2359, 4948, 10502, 22307, 47731, 102367, 220600, 476626, 1033450, 2246252, 4895935, 10694744, 23414838, 51364180, 112891831, 248548836, 548123924, 1210612692, 2677682900, 5930586249, 13151963729, 29201456634
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OFFSET

1,6


COMMENTS

Equivalence is up to rearrangement of the order of elements in both series and parallel configurations.
A series configuration is a multiset of two or more parallel configurations and a parallel configuration is a multiset of two or more series configurations. The unit element is considered to be a parallel configuration.


LINKS



FORMULA

Inverse Euler transform of A339153.


EXAMPLE

In the following examples, elements in series are juxtaposed and elements in parallel are separated by ''. The unit element is denoted by 'o'.
a(1) = 1: (o).
a(4) = 1: (oooo).
a(5) = 1: (ooooo).
a(6) = 3: (oooooo), (oooooo), (oooooo).
a(7) = 4: (ooooooo), (ooo(oooo)), (ooooooo), (ooooooo).


PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))1, #v)}
seq(n)={my(S=vector(n), P=vector(n)); P[1]=1; for(n=2, #S, my(t=EulerT(S[1..n])[n]); S[n]=EulerT(P[1..n])[n]; P[n]=t); P}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



