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 A268148 #27 Feb 11 2016 09:25:11 %S A268148 0,8,768,30720,917504,23592960,553648128,12213813248,257698037760, %T A268148 5257039970304,104453604638720,2031897488130048,38843546786070528, %U A268148 731834939447705600,13618885273168379904,250760427251989217280,4574792530279968800768,82788987402808467652608 %N A268148 A double binomial sum involving absolute values. %C A268148 A fast algorithm follows from Theorem 5 of Brent et al. article. %H A268148 Colin Barker, <a href="/A268148/b268148.txt">Table of n, a(n) for n = 0..800</a> %H A268148 Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, Helmut Prodinger, <a href="http://arxiv.org/abs/1411.1477">Some binomial sums involving absolute values</a>, arXiv:1411.1477v2 [math.CO], 2016. %H A268148 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (48,-768,4096). %F A268148 a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k^2 - l^2)^2). %F A268148 From _Colin Barker_, Feb 11 2016: (Start) %F A268148 a(n) = 2^(4*n-1)*n*(2*n-1). %F A268148 a(n) = 48*a(n-1)-768*a(n-2)+4096*a(n-3) for n>2. %F A268148 G.f.: 8*x*(1+48*x) / (1-16*x)^3. %F A268148 (End) %o A268148 (PARI) a(n) = sum(k=-n,n, sum(l=-n,n, binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k^2 - l^2)^2)); %o A268148 (PARI) concat(0, Vec(8*x*(1+48*x)/(1-16*x)^3 + O(x^20))) \\ _Colin Barker_, Feb 11 2016 %Y A268148 Cf. A000984, A002894, A166337, A254408. %K A268148 easy,nonn %O A268148 0,2 %A A268148 _Richard P. Brent_, Jan 27 2016