%I M0698
%S 1,1,1,2,3,5,8,14,23,41,69,122,208,370,636,1134,1963,3505,6099,10908,
%T 19059,34129,59836,107256,188576,338322,596252,1070534,1890548,
%U 3396570,6008908,10801816,19139155,34422537,61074583,109894294,195217253
%N Number of achiral planted trees with n nodes.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. W. Robinson, F. Harary and A. T. Balaban, <a href="http://dx.doi.org/10.1016/00404020(76)80049X">The numbers of chiral and achiral alkanes and monosubstituted alkanes</a>, Tetrahedron 32 (1976), 355361.
%H R. W. Robinson, F. Harary and A. T. Balaban, <a href="/A000625/a000625.pdf">Numbers of chiral and achiral alkanes and monosubstituted alkanes</a>, Tetrahedron 32 (3) (1976), 355361. (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(0)=1, a(n+1):=sum(s(k)*a(n2*k), k=0..floor(n/2)) (n>=0), where s(n)=A000625(n) (this is eq. (15) in the Robinson et al. paper).  _Emeric Deutsch_, May 16 2004
%p s[0]:=1:s[1]:=1:for n from 0 to 60 do s[n+1/3]:=0 od:for n from 0 to 60 do s[n+2/3]:=0 od:for n from 1 to 55 do s[n+1]:=(2*n/3*s[n/3]+sum(j*s[j]*sum(s[k]*s[njk],k=0..nj),j=1..n))/n od:a[0]:=1: for n from 0 to 50 do a[n+1]:=sum(s[k]*a[n2*k],k=0..floor(n/2)) od:seq(a[j],j=0..45); # here s[n]=A000625(n).
%Y Cf. A000625.
%K nonn
%O 0,4
%A _N. J. A. Sloane_.
%E More terms from _Emeric Deutsch_, May 16 2004
