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 A001895 Number of rooted planar 2-trees with n nodes. (Formerly M1258 N0481) 2
 1, 2, 4, 12, 34, 111, 360, 1226, 4206, 14728, 52024, 185824, 668676, 2424033, 8839632, 32412270, 119410390, 441819444, 1641032536, 6116579352, 22870649308, 85764947502, 322476066224, 1215486756372, 4591838372044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 78, (3.5.28). N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=1..200 F. Harary and E. M. Palmer, Enumeration of self-converse digraphs, Mathematika, 13 (1966), 151-157. FORMULA G.f.: (4-8*x^2-sqrt(1-4*x)-(3+2*x)*sqrt(1-4*x^2))/(8*x^2). a(n) ~ 4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013 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 MATHEMATICA 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 *) CROSSREFS Cf. A000108, A000207. Sequence in context: A148198 A148199 A108530 * A267618 A148200 A148201 Adjacent sequences:  A001892 A001893 A001894 * A001896 A001897 A001898 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Aug 24 2001 STATUS approved

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