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 A115150 #10 May 22 2013 05:47:14
%S A115150 1,15,113,783,5361,36879,255985,1794063,12689393,90505231,650379249,
%T A115150 4705157135,34244198385,250572963855,1842382110705,13605619630095,
%U A115150 100872203796465,750556607938575,5602962592235505,41952165966643215
%N A115150 Third diagonal (M=3) sequence of triangle A113647, called Y(2,1).
%H A115150 Vincenzo Librandi, <a href="/A115150/b115150.txt">Table of n, a(n) for n = 0..300</a>
%F A115150 a(n)= A113647(n+2, n+1), n>=0.
%F A115150 G.f.: ((4*x-2+x^2) + 2*(1-4*x)*c(2*x))/((x^2)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).
%F A115150 Recurrence: (n-1)*(n+3)*a(n) = (7*n^2 + 2*n + 3)*a(n-1) + 4*n*(2*n+1)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A115150 a(n) ~ 2^(3*n+9)/(9*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%t A115150 CoefficientList[Series[((4*x-2+x^2)+2*(1-4*x)*(1-Sqrt[1-8*x])/(4*x))/((x^2)*(1+x)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%Y A115150 a(n)=A115138(n+2), n>=0.
%K A115150 nonn,easy
%O A115150 0,2
%A A115150 _Wolfdieter Lang_, Jan 13 2006