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A052514 Number of labeled trees of height at most 4. 5
0, 1, 2, 9, 64, 625, 7056, 89929, 1284032, 20351601, 354648160, 6736612201, 138472331328, 3061103815081, 72391319923664, 1823032999274985, 48692068509655936, 1374488205290880481, 40877130077266074048 (list; graph; refs; listen; history; text; internal format)
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: A269770 A269649 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

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Last modified November 14 00:05 EST 2019. Contains 329106 sequences. (Running on oeis4.)