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%I M0383 #23 Mar 12 2021 16:50:00
%S 1,2,2,10,14,42,90,354,758,2290,6002,18410,51310,154106,449322,
%T 1384962,4089174,12475362,37746786,116037642,355367310,1097869386,
%U 3393063162,10546081122,32810171382,102465452754,320522209490,1005428474218
%N Symmetries in planted (1,3) trees on 2n vertices.
%D Kathleen A. McKeon, The expected number of symmetries in locally-restricted trees I, pp. 849-860 of Y. Alavi et al., eds., Graph Theory, Combinatorics and Applications. Wiley, NY, 2 vols., 1991.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a003/A003609.java">Java program</a> (github)
%H Kathleen A. McKeon, <a href="/A003609/a003609.pdf">Letter to N. J. A. Sloane, July 25 1991</a>
%H Kathleen A. McKeon, <a href="/A003609/a003609_1.pdf">The expected number of symmetries in locally-restricted trees I</a>, pp. 849-860 of Y. Alavi et al., eds., Graph Theory, Combinatorics and Applications. Wiley, NY, 2 vols., 1991. [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>
%e G.f. = x + 2*x^2 + 2*x^3 + 10*x^4 + 14*x^5 + 42*x^6 + 90*x^7 + ... - _Michael Somos_, Mar 12 2021
%o (PARI) {a(n) = my(A, m); A = x + O(x^2); m = 1; while(n >= (m*=2), A = (1 - sqrt(1 - 2*x*y + y*(y-2)*substvec(A, [x, y], [x^2, y^2])))/y); 2^(n-1) * subst(polcoeff(A, n), y, 1/2)}; /* _Michael Somos_, Mar 12 2021 */
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E More terms from _Sean A. Irvine_, Feb 24 2019
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