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A121355
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Number of transitive PSL_2(ZZ) actions on a finite labeled set of size n.
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5
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1, 1, 8, 48, 120, 2640, 30240, 201600, 4838400, 96163200, 1037836800, 30496435200, 828193766400, 13686991718400, 450537408921600, 15880397524992000, 356398802952192000, 13410127414075392000, 569542360114151424000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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.
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LINKS
| 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
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FORMULA
| If A(z) = g.f. of a(n) and B(z) = g.f. of A121357 then A(z) = log(B(z)).
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MAPLE
| 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);
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CROSSREFS
| Connected version of A121357.
Labeled version of A121350.
Cf. also A005133, A121352, A121356.
Sequence in context: A139279 A067239 A152750 * A168012 A035471 A072819
Adjacent sequences: A121352 A121353 A121354 * A121356 A121357 A121358
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KEYWORD
| nonn
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AUTHOR
| Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006
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