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 A105524 #10 Sep 01 2025 19:58:14
%S A105524 1,-2,2,0,-1,-2,4,4,-10,-12,30,36,-93,-114,300,372,-994,-1244,3364,
%T A105524 4240,-11578,-14676,40400,51448,-142592,-182288,508166,651756,
%U A105524 -1826037,-2348562,6608844,8520564,-24069258,-31097388,88145436,114096096,-324391422,-420590652,1199074584
%N A105524 Diagonal sums of number triangle A105522.
%F A105524 G.f.: ((1+2*x)*sqrt(1+4*x^2)-4*x^2-2*x-1)/(x^2*(sqrt(1+4*x^2)-3)). - amended by _Georg Fischer_, Apr 09 2020
%F A105524 Conjecture: 2*(n+2)*(13*n^2-35*n+6)*a(n) +24*(n-8)*a(n-1) +(91*n^3-375*n^2+152*n+372)*a(n-2) +12*(8-n)*a(n-3) -4*(n-3)*(13*n^2-9*n-16)*a(n-4) = 0. - _R. J. Mathar_, Nov 09 2012
%t A105524 CoefficientList[Series[((1+2*x)*Sqrt[1+4*x^2]-4*x^2-2*x-1)/(x^2*(Sqrt[1+4*x^2]-3)), {x,0,38}], x] (* _Georg Fischer_, Apr 09 2020 *)
%K A105524 easy,sign,changed
%O A105524 0,2
%A A105524 _Paul Barry_, Apr 13 2005