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 A116396 #11 Jun 07 2025 05:21:33
%S A116396 1,2,7,25,93,353,1358,5273,20614,81003,319584,1264924,5019743,
%T A116396 19963699,79541181,317406302,1268283199,5073605801,20316709251,
%U A116396 81427911966,326612013623,1310968893954,5265285993860,21158914176719,85071253608611
%N A116396 Expansion of 2/((2+x)*sqrt(1-4*x)-x).
%C A116396 Diagonal sums of number triangle A116395.
%C A116396 Diagonal sums of the Riordan matrix ((1-sqrt(1-4*x))/(2*x*sqrt(1-4*x)),(1-sqrt(1-4*x))/(2*sqrt(1-4*x))) (A035324). - _Emanuele Munarini_, Apr 26 2011
%F A116396 a(n) = Sum_{k=0..floor(n/2)} (4^(n-k)/2^k)*Sum_{j=0..k} C(k,j)*C(n-k+(j-1)/2,n-k)*(-1)^(k-j).
%F A116396 D-finite with recurrence: +2*n*a(n) +(-13*n+10)*a(n-1) +(9*n-16)*a(n-2) +2*(19*n-41)*a(n-3) +(23*n-66)*a(n-4) +2*(2*n-7)*a(n-5)=0. - _R. J. Mathar_, Jan 24 2020
%t A116396 CoefficientList[Series[(x+(2+x)Sqrt[1-4x])/(2-6x-8x^2-2x^3),{x,0,25}],x] (* _Emanuele Munarini_, Apr 26 2011 *)
%K A116396 easy,nonn
%O A116396 0,2
%A A116396 _Paul Barry_, Feb 12 2006