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

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 60

Formula

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

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 *)

Prog

(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
(Magma) m:=20; R<x>:=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
(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

Crossrefs

Cf. A052513 (height at most 3).

Sequence in context: A269649 A335517 A128577 * A274395 A036776 A036777

Adjacent sequences: A052511 A052512 A052513 * A052515 A052516 A052517

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved