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A339224
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Number of essentially parallel unoriented series-parallel networks with n elements.
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4
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1, 1, 2, 5, 13, 41, 132, 470, 1730, 6649, 26122, 104814, 426257, 1754055, 7282630, 30470129, 128304158, 543303752, 2311904374, 9880776407, 42394198909, 182537610058, 788473887942, 3415782381520, 14837307126498, 64608442956047, 281975101347994, 1233237605651194
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OFFSET
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1,3
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COMMENTS
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See A339225 for additional details.
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LINKS
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FORMULA
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EXAMPLE
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In the following examples of series-parallel networks, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
a(1) = 1: (o).
a(2) = 1: (oo), (o|o).
a(3) = 2: (o|o|o), (o|oo).
a(4) = 5: (o|o|o|o), (o|o|oo), (oo|oo), (o|ooo), (o|o(o|o)).
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PROG
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(PARI) \\ here B(n) gives A003430 as a power series.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
B(n)={my(p=x+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+x)))); p}
seq(n)={my(q=subst(B((n+1)\2), x, x^2), s=x^2+q^2/(1+q), p=x+O(x^2)); for(n=1, n\2, my(t=x + q*(1 + p)); p=x + x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2))) - t); Vec(p+subst(x/(1+x), x, B(n)))/2}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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