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%I M1123 #28 Dec 13 2020 04:33:02
%S 1,1,2,4,8,16,31,62,120,236,454,884,1697,3275,6266,12020,22935,43788,
%T 83325,158516,300914,570794,1081157,2045934,3867617,7304149,13783221,
%U 25984936,48956715,92155376,173376484,325919786,612378787,1149777034
%N Number of partially achiral rooted trees.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vaclav Kotesovec, <a href="/A003240/b003240.txt">Table of n, a(n) for n = 1..3760</a> (terms 1..70 from Herman Jamke)
%H F. Harary and R. W. Robinson, <a href="http://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PID=GDZPPN002191393">The number of achiral trees</a>, J. Reine Angew. Math., 278 (1975), 322-335.
%H F. Harary and R. W. Robinson, <a href="/A002995/a002995_1.pdf">The number of achiral trees</a>, J. Reine Angew. Math., 278 (1975), 322-335. (Annotated scanned copy)
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) ~ c * d^n * n, where d = 1.8332964415228533737988849634129366404833316666328290543862325494628120733... is the root of the equation Sum_{k>=1} A000081(k) / d^(2*k-1) = 1 and c = 0.030410107348865811204534352170117292921782094079168428605205142049899... - _Vaclav Kotesovec_, Dec 13 2020
%o (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=0,100,t(i)*y^(2*i)); p=subst(y*Ty2/(y-Ty2),y,y+y*O(y^n));p=Pol(p,y); r=subst(Ty2*(y+p+(p^2-subst(p,y,y^2))/(2*y))/y^2,y,x+x*O(x^n)); for(i=0,n-2,print1(polcoeff(r,i)","))} - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
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