This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A000553 M5378 N2335 #31 Dec 19 2021 09:37:24
%S A000553 120,2520,43680,757680,13747104,264181680,5395040640,117080049240,
%T A000553 2696387899920,65774992411128,1695845836077120,46110625382246880,
%U A000553 1319345179723609920,39640903618873667040,1248193457738661143808
%N A000553 Number of labeled rooted trees of height 4 with n nodes.
%D A000553 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000553 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000553 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 A000553 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A000553 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A000553 E.g.f.: x*(exp(x*exp(x*exp(x*exp(x)))) - exp(x*exp(x*exp(x)))). - _Vladeta Jovovic_, Jan 29 2008
%p A000553 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 A000553 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 A000553 nonn
%O A000553 5,1
%A A000553 _N. J. A. Sloane_
%E A000553 More terms from _Paul Zimmermann_, Mar 15 1996