cp's OEIS Frontend

A339292 Number of essentially parallel achiral series-parallel networks with n elements and without multiple unit elements in parallel.

%I A339292 #7 Dec 08 2020 02:27:24
%S A339292 1,0,1,2,3,6,11,21,41,79,154,304,598,1188,2360,4719,9431,18966,38107,
%T A339292 76968,155368,314987,638325,1298379,2640223,5385737,10984999,22465570,
%U A339292 45945256,94180208,193076780,396603802,814838739,1676975258,3452212803,7117242628
%N A339292 Number of essentially parallel achiral series-parallel networks with n elements and without multiple unit elements in parallel.
%C A339292 See A339293 for additional details.
%e A339292 In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
%e A339292 a(1) = 1: (o).
%e A339292 a(3) = 1: (o|oo).
%e A339292 a(4) = 2: (o|ooo), (oo|oo).
%e A339292 a(5) = 3: (o|oooo), (oo|ooo), (o|oo|oo).
%e A339292 a(6) = 6: (o|ooooo), (o|o(o|oo)o), (oo|oooo), (ooo|ooo), (o|oo|ooo), (oo|oo|oo).
%o A339292 (PARI) \\ here B(n) gives A339290 as a power series.
%o A339292 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A339292 B(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) ))); p}
%o A339292 seq(n, Z=x)={my(q=subst(B((n+1)\2, Z), x, x^2), s=q^2/(1+q), p=Z+O(x^2), t=0); forstep(n=2, n, 2, t=q*(1 + p); p=Z + (1 + Z)*x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2, -n-1))) - t); Vec(p+O(x*x^n))}
%Y A339292 Cf. A339158, A339289 (oriented), A339291, A339293, A339295 (unoriented).
%K A339292 nonn
%O A339292 1,4
%A A339292 _Andrew Howroyd_, Dec 07 2020