|
%I M1475 #25 Oct 23 2019 08:10:17
%S 1,2,5,15,48,166,596,2221,8472,32995,130507,523100,2119454,8667529,
%T 35727261,148285069,619172847,2599212499,10963049307,46437309218,
%U 197454056586,842504023722,3606195947971,15480329150558,66628688247862,287475949517326,1243140817965661
%N From trees with valency <= 3.
%C Generating function denoted as x(t) = f(V_3;t) - 1 in Cameron page 182. - _Michael Somos_, Jun 13 2014
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. J. Cameron, <a href="http://dx.doi.org/10.1093/qmath/38.2.155">Some treelike objects</a>, Quart. J. Math. Oxford, 38 (1987), 155-183.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F G.f. A(x) satisfies 0 = (1 + x) * A(x)^2 + (2*x - 2) * A(x) + (1 + x) * A(x^2) + 2*x. - _Michael Somos_, Jun 13 2014
%e G.f. = x + 2*x^2 + 5*x^3 + 15*x^4 + 48*x^5 + 166*x^6 + 596*x^7 + 2221*x^8 + ...
%t m = 30; A[_] = 0;
%t Do[A[x_] = (2x + (1+x) A[x]^2 + (1+x) A[x^2])/(2(1-x)) + O[x]^m // Normal, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 23 2019 *)
%o (PARI) {a(n) = my(A); A = x + O(x^2); for(k=2, n, A = truncate(A) + x * O(x^k); A += x - (1-x)*A + (1+x)/2 * (A^2 + subst(A, x, x^2))); polcoeff(A, n)}; /* _Michael Somos_, Jun 13 2014 */
%K nonn
%O 1,2
%A _N. J. A. Sloane_.
%E a(10)-a(37) from _Michael Somos_, Jun 13 2014
|
