A000553 Number of labeled rooted trees of height 4 with n nodes.

120, 2520, 43680, 757680, 13747104, 264181680, 5395040640, 117080049240, 2696387899920, 65774992411128, 1695845836077120, 46110625382246880, 1319345179723609920, 39640903618873667040, 1248193457738661143808

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn

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[ 5378 ] := n -> count(ht(4),size=n)-count(ht(3),size=n): seq(M[ 5378 ](n), n=5..19);

Mathematica

egf = x*(Exp[x*Exp[x*Exp[x*Exp[x]]]] - Exp[x*Exp[x*Exp[x]]]); a[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!; Table[a[n], {n, 5, 19}] (* Jean-François Alcover, Jan 17 2014, after Vladeta Jovovic *)

Formula

E.g.f.: x*(exp(x*exp(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