0,3

Equivalently, the number of PSL_2(ZZ) actions on a finite labeled set of size n.

Also the number of (r,s) pair of permutions in S_n 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 A121355 then A(z) = exp(B(z)).

Six term linear recurrence : (n^3 + 12*n^2 + 47*n + 61)*a(n + 6) = (29040 + 239224*n^2 + 127628*n + 20715*n^6 + 252267*n^3 + 166304*n^4 + 71889*n^5 + 33*n^9 + 3943*n^7 + 476*n^8 + n^10)*a(n) + (441*n^4 + 3*n^6 + 2160 + 57*n^5 + 4572*n + 3948*n^2 + 1779*n^3)*a(n + 1) + (34920 + 61314*n + 45886*n^2 + 18989*n^3 + 4697*n^4 + 695*n^5 + 57*n^6 + 2*n^7)*a(n + 2) + (19640 + 79*n^5 + 3*n^6 + 861*n^4 + 27598*n + 16084*n^2 + 4975*n^3)*a(n + 3) + (17*n^3 + 425 + n^4 + 350*n + 113*n^2)*a(n + 4) + (1 + 20*n + 9*n^2 + n^3)*a(n + 5) with n = 0, 1, ...

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) : sort(add(op(n+1, exs23)*n!, n=0..N), t, ascending);

Unconnected version of A121355.

Labeled version of A121352.

Labeled, unconnected version of A121350.

Cf. also A005133, A121356.

Sequence in context: A055531 A059435 A079858 this_sequence A098926 A074610 A103882

Adjacent sequences: A121354 A121355 A121356 this_sequence A121358 A121359 A121360

nonn

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