A000553 - OEIS

%I M5378 N2335 #31 Dec 19 2021 09:37:24

%S 120,2520,43680,757680,13747104,264181680,5395040640,117080049240,

%T 2696387899920,65774992411128,1695845836077120,46110625382246880,

%U 1319345179723609920,39640903618873667040,1248193457738661143808

%N Number of labeled rooted trees of height 4 with n nodes.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F E.g.f.: x*(exp(x*exp(x*exp(x*exp(x)))) - exp(x*exp(x*exp(x)))). - _Vladeta Jovovic_, Jan 29 2008

%p 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);

%t 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_ *)

%K nonn

%O 5,1

%A _N. J. A. Sloane_

%E More terms from _Paul Zimmermann_, Mar 15 1996