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 A000524 M1927 N0761 #38 Mar 23 2023 23:09:32
%S A000524 2,9,34,119,401,1316,4247,13532,42712,133816,416770,1291731,3987444,
%T A000524 12266845,37627230,115125955,351467506,1070908135,3257389088,
%U A000524 9892759091,30002923380,90879555521,274963755791,831064788976
%N A000524 Number of rooted trees with n nodes, 2 of which are labeled.
%D A000524 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.
%D A000524 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000524 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000524 T. D. Noe, <a href="/A000524/b000524.txt">Table of n, a(n) for n=2..200</a>
%H A000524 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A000524 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A000524 G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107.
%F A000524 G.f.: A(x) = B(x)^2*(2-B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - _Vladeta Jovovic_, Oct 19 2001
%p A000524 b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n,k) option remember; add(b(n+1-j*k), j=1..iquo(n,k)) end: B:= proc(n) option remember; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-1)^2*(2-B(n-1))/(1-B(n-1))^3, x=0, n+1), x,n): seq(a(n), n=2..25); # _Alois P. Heinz_, Aug 21 2008
%t A000524 b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[b[n+1 - j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := Coefficient[Series[B[n-1]^2*((2 - B[n-1])/ (1 - B[n-1])^3), {x, 0, n+1}], x, n]; Table[a[n], {n, 2, 25}] (* _Jean-François Alcover_, Dec 20 2012, translated from _Alois P. Heinz_'s Maple program *)
%Y A000524 Column k=2 of A008295.
%K A000524 nonn,easy,nice
%O A000524 2,1
%A A000524 _N. J. A. Sloane_
%E A000524 More terms, new description and formula from _Christian G. Bower_, Nov 15 1999