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 A115256 #21 Jan 22 2025 05:23:49
%S A115256 1,2,8,25,90,312,1145,4186,15640,58681,222298,845848,3235385,12418650,
%T A115256 47827992,184688185,714884186,2772776984,10774163001,41932100698,
%U A115256 163430680600,637793652281,2491918144602,9746480252952,38157725306425
%N A115256 Diagonal sums of correlation triangle of central binomial coefficients.
%C A115256 Diagonal sums of number triangle A115255.
%H A115256 G. C. Greubel, <a href="/A115256/b115256.txt">Table of n, a(n) for n = 0..1000</a>
%F A115256 G.f.: 1/(sqrt(1-4*x)*sqrt(1-4*x^2)*(1-x^3)).
%F A115256 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} [j<=k]*C(2*k-2*j, k-j)*[j<=n-2*k]*C(2*n-4*k-2*j, n-2*k-j).
%F A115256 a(n) ~ sqrt(3) * 2^(2*n+7) / (189 * sqrt(Pi*n)). - _Vaclav Kotesovec_, Mar 02 2014
%F A115256 Conjecture: n*a(n) + 2*(-2*n+1)*a(n-1) + 4*(-n+1)*a(n-2) + 3*(5*n-8)*a(n-3) + 2*(2*n-1)*a(n-4) + 4*(n-1)*a(n-5) + 8*(-2*n+3)*a(n-6) = 0. - _R. J. Mathar_, Jun 22 2016
%t A115256 CoefficientList[Series[1/((Sqrt[1-4x])(Sqrt[1-4x^2])(1-x^3)), {x,0,30}], x] (* _Harvey P. Dale_, Feb 15 2012 *)
%o A115256 (PARI) my(x='x+O('x^50)); Vec(1/(sqrt(1-4*x)*sqrt(1-4*x^2)*(1-x^3))) \\ _G. C. Greubel_, Mar 18 2017
%K A115256 easy,nonn
%O A115256 0,2
%A A115256 _Paul Barry_, Jan 18 2006