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 A052322 #18 Jun 22 2018 23:20:32
%S A052322 1,2,9,40,385,4536,66409,1127792,21981537,483858640,11873508361,
%T A052322 321497975448,9522483900241,306292854886760,10632656242583145,
%U A052322 396223803663328096,15776491521834720961,668460175137505993248,30030668624358362706697,1425868954034374729854920
%N A052322 Number of labeled rooted trees with a forbidden limb of length 3.
%C A052322 A rooted tree with a forbidden limb of length k is a rooted tree where the path from any leaf inward hits a branching node or the root within k steps.
%H A052322 Alois P. Heinz, <a href="/A052322/b052322.txt">Table of n, a(n) for n = 1..390</a>
%H A052322 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A052322 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A052322 E.g.f. satisfies A(x) = x*exp(A(x) - x^3).
%F A052322 E.g.f: -LambertW(-x*exp(-x^3)). - _Vaclav Kotesovec_, Jan 08 2014
%F A052322 a(n) ~ sqrt(1+LambertW(-3*exp(-3))) * n^(n-1) * exp(n/3*LambertW(-3*exp(-3))). - _Vaclav Kotesovec_, Jan 08 2014
%t A052322 Rest[CoefficientList[Series[-LambertW[-x*E^(-x^3)], {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Jan 08 2014 *)
%Y A052322 Cf. A002955, A002988-A002992, A052319-A052329.
%K A052322 nonn,eigen
%O A052322 1,2
%A A052322 _Christian G. Bower_, Dec 15 1999