A000553 Number of labeled rooted trees of height 4 with n nodes. (Formerly M5378 N2335)

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

Offset

5,1

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=5..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*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[ 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 *)

Crossrefs

Sequence in context: A267839 A220050 A032180 * A126232 A105943 A219945

Adjacent sequences: A000550 A000551 A000552 * A000554 A000555 A000556

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Paul Zimmermann, Mar 15 1996

Status

approved