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 A125307 #29 Sep 07 2018 03:05:38
%S A125307 1,1,4,15,80,480,3444,27790,253504,2556792,28382880,343071168,
%T A125307 4490999424,63253633872,954133373088,15343385194800,262060291958784,
%U A125307 4737396899952384,90370907329842432,1814141041750834560,38229440785429201920,843786230514306621696
%N A125307 Number of increasing trees with branches of height 1.
%D A125307 R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, 1997. Proposition 1.3.16, p. 25.
%H A125307 G. C. Greubel, <a href="/A125307/b125307.txt">Table of n, a(n) for n = 1..448</a>
%H A125307 Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F A125307 E.g.f.: (x-1+log(1-x)) / ( (x-1)^2 (log(1-x)-1) ).
%F A125307 a(n) = n!*(sum((-1)^(m)*(n-m+1)/(m-1)!*sum(k!*Stirling1(m-1,k),k,1,m-1),m,2,n)+1). - _Vladimir Kruchinin_, Sep 09 2010
%F A125307 a(n) ~ n!*n*(1 - 1/log(n) + gamma/log(n)^2), where gamma is Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Sep 25 2013
%t A125307 Range[0, 21]!CoefficientList[ Series[(x - 1 + Log[1 - x])/((1 - x)^2(Log[1 - x] - 1)), {x, 0, 21}], x] (* _Robert G. Wilson v_, Jan 26 2007 *)
%o A125307 (Maxima) a(n):=n!*(sum((-1)^(m)*(n-m+1)/(m-1)!*sum(k!*stirling1(m-1,k), k,1,m-1), m,2,n)+1); /* _Vladimir Kruchinin_, Sep 09 2010 */
%o A125307 (PARI) x='x+O('x^30); Vec(serlaplace( (x-1+log(1-x))/((x-1)^2*(log(1-x) -1)))) \\ _G. C. Greubel_, Sep 05 2018
%K A125307 nonn
%O A125307 1,3
%A A125307 _Wenjin Woan_, Jan 17 2007
%E A125307 More terms from _N. J. A. Sloane_, Jan 26 2007