A000552 Number of labeled rooted trees of height 3 with n nodes. (Formerly M5159 N2241)

24, 300, 3360, 38850, 475776, 6231960, 87530400, 1316954430, 21173760960, 362670636900, 6596214691248, 126980000240730, 2579214238608000, 55118036257959600, 1235935135837111104, 29009023670878484598

Offset

4,1

References

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

Table of n, a(n) for n=4..19.

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Formula

E.g.f.: x*(exp(x*exp(x*exp(x)))-exp(x*exp(x))). - Vladeta Jovovic, Jan 29 2008

Maple

ht := proc(m) local i; [ T0, {seq(T.i=Prod(Z, Set(T.(i+1))), i=0..m-1), T.m=Z}, labeled ] end: M[ 5159 ] := n -> count(ht(3), size=n)-count(ht(2), size=n): seq(M[ 5159 ](n), n=4..19);

Mathematica

With[{nn=20}, Drop[CoefficientList[Series[x(Exp[x Exp[x Exp[x]]]- Exp[x Exp[x]]), {x, 0, nn}], x]Range[0, nn]!, 4]] (* Harvey P. Dale, Oct 01 2011 *)

Crossrefs

Sequence in context: A014103 A321953 A206002 * A233876 A171742 A187851

Adjacent sequences: A000549 A000550 A000551 * A000553 A000554 A000555

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Paul Zimmermann, Mar 15 1996

Status

approved