A003092 Number of labeled plane 2-trees with n nodes. (Formerly M2159)

0, 1, 2, 36, 1200, 57000, 3477600, 257826240, 22438563840, 2238543216000, 251584613280000, 31431367287936000, 4319334744012288000, 647313578549730892800, 105041172967733882880000, 18345770194541665075200000, 3430869798262479024291840000

Offset

1,3

References

F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.14.

E. M. Palmer and R. C. Read, on the number of plane 2-trees, J. Lond. Math. Soc., 6 (1973), 583-592.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 1..300

Allan Bickle,  A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.

E. M. Palmer and R. C. Read, On the number of plane 2-trees, J. Lond. Math. Soc., 6 (1973), 583-592. [Annotated and corrected scanned copy]

Index entries for sequences related to trees

Formula

a(n) = n*(n-1)^2*(5*n-10)!/(4*n-6)!.

Maple

[0, seq(n*(n-1)^2*(5*n-10)!/(4*n-6)!, n=2..20) ];

Mathematica

Join[{0}, Table[n*(n-1)^2*(5*n-10)!/(4*n-6)!, {n, 2, 30}]] (* G. C. Greubel, Nov 02 2022 *)

Prog

(Magma) [0] cat [n*(n-1)^2*Factorial(5*n-10)/Factorial(4*n-6): n in [2..30]]; // G. C. Greubel, Nov 02 2022
(SageMath) [0]+[n*(n-1)^2*factorial(5*n-10)/factorial(4*n-6) for n in range(2, 30)] # G. C. Greubel, Nov 02 2022

Crossrefs

Sequence in context: A210899 A302903 A259467 * A187535 A263421 A046673

Adjacent sequences: A003089 A003090 A003091 * A003093 A003094 A003095

Keyword

nonn

Author

N. J. A. Sloane

Status

approved