OFFSET
1,3
COMMENTS
Equivalently, the number of isomorphism class of transitive PSL_2(Z) actions on a finite dotted (i.e., having a distinguished element) set of size n. Also the number of different connected dotted trivalent diagrams of size n. - Samuel A. Vidal, Jul 23 2006
Connected and dotted version of A121352. Dotted version of A121350. Unlabeled version of A121356. Unlabeled and dotted version of A121355. - Samuel A. Vidal, Jul 23 2006
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Morris Newman, Classification of Normal Subgroups of the Modular Group, Transactions of the American Mathematical Society 126 (1967), no. 2, 267-277.
Morris Newman, Asymptotic formulas related to free products of cyclic groups, Math. Comp. 30 (1976), no. 136, 838-846.
S. A. Vidal, Sur la Classification et le Denombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison, (in French), arXiv:math/0702223 [math.CO], 2007.
FORMULA
If A(z) = g.f. of a(n) and B(z) = g.f. of A121356 then A(z) is the Borel transform of B(z). - Samuel A. Vidal, Jul 23 2006
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) ; # Samuel A. Vidal, Jul 23 2006
MATHEMATICA
m = 50; exs2 = Series[ Exp[t + t^2/2], {t, 0, m+1}] // Normal; exs3 = Series[ Exp[t + t^3/3], {t, 0, m+1}] // Normal; exs23 = Sum[ exs2[[n+1]]*exs3[[n+1]]/(t^n/n!), {n, 0, m}]; logexs23 = Series[ Log[exs23], {t, 0, m+1}] // Normal; CoefficientList[ Sum[ logexs23[[n]]*n, {n, 1, m}], t] // Rest (* Jean-François Alcover, Dec 05 2012, translated from Maple *)
PROG
(PARI) N=50; x='x+O('x^(N+1));
A121357_ser = serconvol(serlaplace(exp(x+x^2/2)), serlaplace(exp(x+x^3/3)));
Vec(x*log(serconvol(A121357_ser, exp(x)))') \\ Gheorghe Coserea, May 10 2017
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Samuel A. Vidal, Jul 23 2006
Entry revised by N. J. A. Sloane, Jul 25 2006
STATUS
approved