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 A121356 Number of transitive PSL_2(ZZ) actions on a finite dotted and labeled set of size n. 5
 1, 2, 24, 192, 600, 15840, 211680, 1612800, 43545600, 961632000, 11416204800, 365957222400, 10766518963200, 191617884057600, 6758061133824000, 254086360399872000, 6058779650187264000, 241382293453357056000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS S. A. Vidal, Sur la Classification et le Dénombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison, (in French), arXiv:math/0702223 [math.CO], 2006. 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). 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); MATHEMATICA m = 18; s2 = Exp[t + t^2/2] + O[t]^(m+1) // Normal; s3 = Exp[t + t^3/3] + O[t]^(m+1) // Normal; s = Sum[s2[[n+1]] s3[[n+1]]/(t^n/n!), {n, 0, m}]; CoefficientList[Log[s] + O[t]^(m+1), t] Range[0, m]! Range[0, m] // Rest (* Jean-François Alcover, Sep 02 2018, from Maple *) PROG (PARI) N=18; x='x+O('x^(N+1)); A121357_ser = serconvol(serlaplace(exp(x+x^2/2)), serlaplace(exp(x+x^3/3))); A121355_ser = serlaplace(log(serconvol(A121357_ser, exp(x)))); Vec(x*A121355_ser') \\ Gheorghe Coserea, May 10 2017 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 A245019 A189769 Adjacent sequences:  A121353 A121354 A121355 * A121357 A121358 A121359 KEYWORD nonn AUTHOR Samuel A. Vidal, Jul 23 2006 STATUS approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)