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 A103138 #15 Feb 13 2014 13:15:20
%S A103138 0,1,-3,10,-38,158,-698,3218,-15310,74614,-370610,1869338,-9549174,
%T A103138 49302030,-256859754,1348695330,-7129819038,37916710374,-202708895330,
%U A103138 1088819681834,-5873129780422,31800514324606,-172780691083034,941714095635890,-5147414826440558,28210011946820438
%N A103138 Second column of inverse of Delannoy triangle.
%C A103138 The positive sequence has g.f. (1+x*S(x))*x*S(x).
%C A103138 Second column of A103136.
%H A103138 Vincenzo Librandi, <a href="/A103138/b103138.txt">Table of n, a(n) for n = 0..200</a>
%F A103138 G.f.: (1-x*S(-x))*x*S(-x), where S(x) is the g.f. of the large Schroeder numbers A006318.
%F A103138 Conjecture: 2*n*a(n) +(13*n-20)*a(n-1) +(8*n-27)*a(n-2) +(n-5)*a(n-3)=0. - _R. J. Mathar_, Dec 14 2011
%F A103138 G.f.: x = Sum_{n>=1} a(n) * x^n * (1+x)^n / (1-x)^(n+1). - _Paul D. Hanna_, Aug 06 2013
%F A103138 G.f. satisfies: A(x*(1+x)/(1-x)) = x - x^2. - _Paul D. Hanna_, Aug 06 2013
%F A103138 a(n) ~ (-1)^n * (1-2*sqrt(2)) * sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Feb 01 2014
%e A103138 G.f.: A(x) = x - 3*x^2 + 10*x^3 - 38*x^4 + 158*x^5 - 698*x^6 + ... where A( x*(1+x)/(1-x) ) / (1-x) = x.
%t A103138 CoefficientList[Series[(1-x*(1+x-(1+6*x+x^2)^(1/2))/(-2*x))*x*(1+x-(1+6*x+x^2)^(1/2))/(-2*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 01 2014 *)
%o A103138 (PARI) {a(n)=if(n==1, 1, -polcoeff(sum(k=1, n-1, a(k)*x^k*(1+x)^k/(1-x+x*O(x^n))^(k+1)), n))} \\ _Paul D. Hanna_, Aug 06 2013
%K A103138 easy,sign
%O A103138 0,3
%A A103138 _Paul Barry_, Jan 24 2005