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 A186828 #10 Feb 13 2015 17:28:38
%S A186828 1,1,4,14,57,247,1124,5296,25621,126529,635264,3232886,16638821,
%T A186828 86456767,452927448,2389672752,12686560409,67721774737,363268546892,
%U A186828 1957131383342,10585610149121,57458399978455,312890905815900,1708883398754176,9358483855106829,51378142520487281,282714583026982504
%N A186828 Diagonal sums of number triangle A186826.
%F A186828 G.f.: (1+x-3x^2+x^3-(1+x^2)*sqrt(1-6x+x^2))/(4x(1-x+x^2+x^3)).
%F A186828 Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(9*n-7)*a(n-2) +(-13*n+36)*a(n-3) +(3*n-35)*a(n-4) +(-5*n+28)*a(n-5) +(-5*n+21)*a(n-6) +(n-6)*a(n-7)=0. - _R. J. Mathar_, Feb 13 2015
%t A186828 CoefficientList[Series[(1+x-3x^2+x^3-(1+x^2)Sqrt[1-6x+x^2])/(4x(1-x+ x^2+ x^3)),{x,0,30}],x] (* _Harvey P. Dale_, Aug 23 2011 *)
%K A186828 nonn,easy
%O A186828 0,3
%A A186828 _Paul Barry_, Feb 27 2011