A052514 Number of labeled trees of height at most 4.

0, 1, 2, 9, 64, 625, 7056, 89929, 1284032, 20351601, 354648160, 6736612201, 138472331328, 3061103815081, 72391319923664, 1823032999274985, 48692068509655936, 1374488205290880481, 40877130077266074048

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 60

Crossrefs

Cf. A052513 (height at most 3).

Programs

Magma

m:=20; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( x*Exp(x*Exp(x*Exp(x*Exp(x)))) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, May 13 2019

Maple

spec := [S,{T2=Prod(Z,Set(T3)),S=Prod(Z,Set(T1)), T4=Z, T3=Prod(Z,Set(T4)), T1=Prod(Z,Set(T2))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

With[{nn=20},CoefficientList[Series[x*Exp[x*Exp[x*Exp[x*Exp[x]]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 23 2018 *)

PARI

my(x='x+O('x^20)); concat(0, Vec(serlaplace( x*exp(x*exp(x*exp(x*exp(x)))) ))) \\ G. C. Greubel, May 13 2019

Sage

m = 20; T = taylor(x*exp(x*exp(x*exp(x*exp(x)))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 13 2019

Formula

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

Extensions

Added "at most" in the title; by Stanislav Sykora, May 12 2012