1,4

The g.f. (1-z**2-2*z**3-8*z**4+7*z**5+4*z**6)/(1-z-z**2-2*z**3-6*z**4+14*z**5) was conjectured by Simon Plouffe in his 1992 dissertation, but this is incorrect.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vaclav Kotesovec, Table of n, a(n) for n = 1..3770 (terms 1..73 from Herman Jamke)

F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.

F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335. (Annotated scanned copy)

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

a(n) ~ c * d^n, where d = 1.8332964415228533737988849634129366404833316666328290543862325494628120733... is the root of the equation Sum_{k>=1} A000081(k) / d^(2*k-1) = 1 and c = 0.123308773712306885475561730669251048497115967922743533462465528423705228... - Vaclav Kotesovec, Dec 13 2020

(PARI) t(n)=local(A=x); if(n<1, 0, for(k=1, n-1, A/=(1-x^k+x*O(x^n))^polcoeff(A, k)); polcoeff(A, n)) {n=100; Ty2=sum(i=0, n, t(i)*y^(2*i)); p=subst(y*Ty2/(y-Ty2), y, y+y*O(y^n)); p=Pol(p, y); a=subst(Ty2*(y+p+(p^2-subst(p, y, y^2))/(2*y))/y^2-(p^2+subst(p, y, y^2))/(2*y^2)+Ty2, y, x+x*O(x^n)); for(i=0, n-2, print1(polcoeff(a, i)", "))} \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008

Sequence in context: A193196 A319755 A309807 * A320160 A055873 A246565

Adjacent sequences: A003240 A003241 A003242 * A003244 A003245 A003246

nonn,easy

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008

approved