1,3

Equivalently, the number of different connected labeled trivalent diagrams of size n.

Also the number of (r,s) pair of permutions in S_n, which generate a transitive action and for which r is involutive i.e. r^2 = id and s is of weak order three i.e. s^3 = id.

S. A. Vidal, Sur la Classification et le Denombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison (in French), 2006, http://arXiv.org/abs/math.CO/0702223

If A(z) = g.f. of a(n) and B(z) = g.f. of A121357 then A(z) = log(B(z)).

N := 100 : exs2:=sort(convert(taylor(exp(t+t^2/2), t, N+1), polynom), t, ascending) : exs3:=sort(convert(taylor(exp(t+t^3/3), t, N+1), polynom), t, ascending) : exs23:=sort(add(op(n+1, exs2)*op(n+1, exs3)/(t^n/ n!), n=0..N), t, ascending) : logexs23:=sort(convert(taylor(log(exs23), t, N+1), polynom), t, ascending) : sort(add(op(n, logexs23)*n!, n=1..N), t, ascending);

Connected version of A121357.

Labeled version of A121350.

Cf. also A005133, A121352, A121356.

Sequence in context: A121028 A139279 A067239 this_sequence A035471 A072819 A073912

Adjacent sequences: A121352 A121353 A121354 this_sequence A121356 A121357 A121358

nonn

Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006