A001895 Number of rooted planar 2-trees with n nodes. (Formerly M1258 N0481)

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

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.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

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: A148199 A343663 A108530 * A267618 A148200 A148201

Adjacent sequences: A001892 A001893 A001894 * A001896 A001897 A001898

Keyword

nonn,nice,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vladeta Jovovic, Aug 24 2001

Status

approved