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 A083862 #8 Dec 26 2019 04:46:12 %S A083862 0,1,3,10,39,171,819,4229,23247,135088,824163,5255361,34876647, %T A083862 240130801,1710323667,12572548582,95183606559,740843916471, %U A083862 5918533467075,48463830575837,406239439253175,3481899731310196 %N A083862 Main diagonal of array A083857. %F A083862 a(n) = (((3 + sqrt(4*n + 1))/2)^n - ((3 - sqrt(4*n + 1))/2)^n)/sqrt(4*n + 1). %p A083862 T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := 3*T(n, k - 1) + (n - 2)*T(n, k - 2); end if; v; end proc; %p A083862 seq(T(n, n), n = 0 .. 40); # _Petros Hadjicostas_, Dec 25 2019 %Y A083862 Cf. A083857, A083859, A083863. %K A083862 easy,nonn %O A083862 0,3 %A A083862 _Paul Barry_, May 06 2003