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A001895 Number of rooted planar 2-trees with n nodes.

%I A001895 M1258 N0481 #32 Jul 08 2025 16:27:08
%S A001895 1,2,4,12,34,111,360,1226,4206,14728,52024,185824,668676,2424033,
%T A001895 8839632,32412270,119410390,441819444,1641032536,6116579352,
%U A001895 22870649308,85764947502,322476066224,1215486756372,4591838372044
%N A001895 Number of rooted planar 2-trees with n nodes.
%D A001895 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 78, (3.5.28).
%D A001895 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001895 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001895 T. D. Noe, <a href="/A001895/b001895.txt">Table of n, a(n) for n=1..200</a>
%H A001895 F. Harary and E. M. Palmer, <a href="http://dx.doi.org/10.1112/S0025579300003910">Enumeration of self-converse digraphs</a>, Mathematika, 13 (1966), 151-157.
%H A001895 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A001895 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A001895 G.f.: (4-8*x^2-sqrt(1-4*x)-(3+2*x)*sqrt(1-4*x^2))/(8*x^2).
%F A001895 a(n) ~ 4^n/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Aug 13 2013
%F A001895 Recurrence: (n+1)*(n+2)*(8*n^3 - 43*n^2 + 67*n - 36)*a(n) = 4*n*(n+1)*(8*n^3 - 39*n^2 + 41*n - 3)*a(n-1) + 4*(8*n^5 - 43*n^4 + 80*n^3 - 26*n^2 - 61*n + 36)*a(n-2) - 8*(n-3)*(2*n-3)*(8*n^3 - 19*n^2 + 5*n - 4)*a(n-3). - _Vaclav Kotesovec_, Aug 13 2013
%t A001895 Rest[CoefficientList[Series[(4-8x^2-Sqrt[1-4x]-(3+2x)Sqrt[1-4x^2])/ (8x^2),{x,0,30}],x]] (* _Harvey P. Dale_, Aug 08 2011 *)
%Y A001895 Cf. A000108, A000207.
%K A001895 nonn,nice,easy
%O A001895 1,2
%A A001895 _N. J. A. Sloane_
%E A001895 More terms from _Vladeta Jovovic_, Aug 24 2001