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 A108522 #20 Jan 20 2025 08:38:58
%S A108522 1,2,9,70,771,10948,190205,3907494,92654059,2490459468,74827519077,
%T A108522 2485153213814,90403692195179,3574835773247140,152675377606343901,
%U A108522 7003761877546096278,343454890456254782203,17929588055863943650988
%N A108522 Number of increasing rooted trees with n generators.
%C A108522 A generator is a leaf or a node with just one child.
%C A108522 In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
%H A108522 Vaclav Kotesovec, <a href="/A108522/b108522.txt">Table of n, a(n) for n = 1..250</a>
%H A108522 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A108522 E.g.f. satisfies: 2*A(x) = x - 1 + exp(A(x)) + Integral A(x) dx. - corrected by _Vaclav Kotesovec_ and _Paul D. Hanna_, Mar 29 2014
%F A108522 From _Paul D. Hanna_, Mar 29 2014: (Start)
%F A108522 E.g.f. satisfies: A(x) = A'(x)*(2 - exp(A(x))) - 1.
%F A108522 E.g.f. satisfies: A'(x) = (1 + A(x))/(2 - exp(A(x))).
%F A108522 (End)
%F A108522 a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.3160173586544089316502903103262192204293322854083... and c = 0.51723490785798357350192800634304... - _Vaclav Kotesovec_, Mar 29 2014
%o A108522 (PARI) {a(n)=local(A=x);for(i=1,n,A=intformal((1+A)/(2-exp(A+x*O(x^n)))) );n!*polcoeff(A,n)}
%o A108522 for(n=1,20,print1(a(n),", ")) \\ _Paul D. Hanna_, Mar 29 2014
%Y A108522 Cf. A108521-A108529, A007151, A001147.
%K A108522 nonn
%O A108522 1,2
%A A108522 _Christian G. Bower_, Jun 07 2005