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A339289
Number of essentially parallel oriented series-parallel networks with n elements and without multiple unit elements in parallel.
5
1, 0, 1, 2, 5, 14, 39, 117, 353, 1099, 3458, 11066, 35738, 116622, 383448, 1269869, 4230557, 14170956, 47693457, 161207066, 546987882, 1862464911, 6361729689, 21793247587, 74855427331, 257743707769, 889477338903, 3076038022778, 10658447368514, 36998473045302
OFFSET
1,4
COMMENTS
See A339290 for additional details.
FORMULA
G.f.: B(x)/(1 + B(x)) where B(x) is the g.f. of A339290.
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(3) = 1: (o|oo).
a(4) = 2: (o|ooo), (oo|oo).
a(5) = 5: (o|oooo), (o|o(o|oo)), (o|(o|oo)o), (oo|ooo), (o|oo|oo).
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = Z + (1 + Z)*x*Ser(EulerT( Vec(p^2/(1+p), -n) ))); Vec(1-1/(1+p))}
CROSSREFS
Cf. A339155, A339288, A339290, A339292 (achiral), A339295 (unoriented).
Sequence in context: A102406 A307754 A151409 * A003054 A317553 A370723
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 07 2020
STATUS
approved