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 A071213 #7 Mar 25 2016 06:57:22 %S A071213 1,4,34,436,7428,157368,3980688,116949600,3911421600,146673662400, %T A071213 6093249563520,277729608280320,13778539159795200,739059210587980800, %U A071213 42615627311477606400,2628646012982829772800,172704619437756321484800 %N A071213 Number of labeled planar trees with n nodes such that the root is smaller than all its children. %H A071213 C. Chauve, S. Dulucq and O. Guibert, <a href="http://www.cecm.sfu.ca/~cchauve/Publications/RR-1226-99.ps">Enumeration of some labeled trees</a>, research report RR-1226-99, LaBRI, Bordeaux I University, 1999. %F A071213 E.g.f.: F(C(x))+x*[F(C(x))]', where C(x)/x is g.f. of Catalan numbers (A000108), F(x)=1+log(1-x)/x-log(1-x). - _Vladimir Kruchinin_, Mar 23 2016 %p A071213 n -> 2 * sum((n-1) * (n-2+k)! / (k! * (n-1-k)), k=0 .. n-2) - ((2*n-3)! / (n-2)!); %o A071213 (Maxima) %o A071213 C(x):=(1-sqrt(1-4*x))/(2); %o A071213 F(x):=1+log(1-x)/x-log(1-x); %o A071213 makelist(n!*coeff(taylor(F(C(x))+x*diff(F(C(x)),x),x,0,15),x,n),n,1,15); /*_Vladimir Kruchinin_, Mar 23 2016 */ %Y A071213 Cf. A000108, A000312, A033184. %K A071213 easy,nonn %O A071213 2,2 %A A071213 Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002