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A121356
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Number of transitive PSL_2(ZZ) actions on a finite dotted and labeled set of size n.
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5
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1, 2, 24, 192, 600, 15840, 211680, 1612800, 43545600, 961632000, 11416204800, 365957222400, 10766518963200, 191617884057600, 6758061133824000, 254086360399872000, 6058779650187264000, 241382293453357056000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| "Dotted" means having a distinguished element. - N. J. A. Sloane, Feb 06 2012
Equivalently, the number of different connected, dotted and labeled trivalent diagrams of size n.
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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
| a(n) = A121355(n)*n.
If A(z) = g.f. of a(n) and B(z) = g.f. of A121355 then A(z) = z d/dz B(z) (Euler operator).
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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, n=1..N), t, ascending);
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CROSSREFS
| Labeled version of A005133.
Labeled and dotted version of A121350.
Dotted version of A121355.
Connected and dotted version of A121357.
Connected, labeled and dotted version of A121352.
Sequence in context: A131972 A059387 A126190 * A052780 A189769 A174668
Adjacent sequences: A121353 A121354 A121355 * A121357 A121358 A121359
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KEYWORD
| nonn,changed
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AUTHOR
| Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006
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