A000552 Number of labeled rooted trees of height 3 with n nodes.

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

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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

• 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

Programs

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 *)

Formula

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

Extensions

More terms from Paul Zimmermann, Mar 15 1996