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 A387467 #16 Sep 01 2025 11:03:26
%S A387467 1,2,14,128,2566,44752,1523724,39267328,1893328966,64541150912,
%T A387467 4029767542756,170848520912896,13100724115628956,664175960969073152,
%U A387467 60396776494002647768,3563049510869692907520,374818464874078558810694,25220474024437034383526912,3012865557320147302034729844
%N A387467 a(n) = Sum_{k=0..n} (1-n*i)^k * (1+n*i)^(n-k) * binomial(n,k)^2, where i is the imaginary unit.
%H A387467 Vincenzo Librandi, <a href="/A387467/b387467.txt">Table of n, a(n) for n = 0..400</a>
%F A387467 a(n) = Sum_{k=0..floor(n/2)} n^(2*k) * binomial(2*(n-k),n-k) * binomial(n-k,k).
%F A387467 a(n) = Sum_{k=0..floor(n/2)} (n^2+1)^k * 2^(n-2*k) * binomial(n,2*k) * binomial(2*k,k).
%F A387467 a(n) = [x^n] (1 + 2*x + (n^2+1)*x^2)^n.
%t A387467 Table[Sum[(n^2+1)^k*2^(n-2*k)*Binomial[n,2*k]*Binomial[2*k,k],{k,0,Floor[n/2]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387467 (PARI) a(n) = sum(k=0, n\2, (n^2+1)^k*2^(n-2*k)*binomial(n, 2*k)*binomial(2*k, k));
%o A387467 (Magma) [(&+[n^(2*k) * Binomial(2*(n-k),n-k) * Binomial(n-k,k): k in [0..Floor(n/2)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 01 2025
%Y A387467 Main diagonal of A387466.
%Y A387467 Cf. A387430.
%K A387467 nonn,new
%O A387467 0,2
%A A387467 _Seiichi Manyama_, Aug 29 2025