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 A386918 #22 Aug 15 2025 17:56:26
%S A386918 1,8,112,1760,29120,496128,8614144,151557120,2692684800,48201359360,
%T A386918 868004380672,15706806542336,285362317180928,5202031080243200,
%U A386918 95104728494899200,1743063914667048960,32016101348447354880,589188508080622534656,10861173739509105295360
%N A386918 a(n) = 2^n * binomial(4*n,n).
%H A386918 Vincenzo Librandi, <a href="/A386918/b386918.txt">Table of n, a(n) for n = 0..350</a>
%F A386918 a(n) = Sum_{k=0..n} binomial(4*n,k) * binomial(4*n-k,n-k).
%F A386918 a(n) = [x^n] (1+x)^(4*n)/(1-x)^(3*n+1).
%F A386918 a(n) = [x^n] 1/(1-2*x)^(3*n+1).
%F A386918 a(n) = [x^n] (1+2*x)^(4*n).
%t A386918 Table[2^n*Binomial[4*n,n],{n,0,30}] (* _Vincenzo Librandi_, Aug 11 2025 *)
%o A386918 (PARI) a(n) = 2^n*binomial(4*n, n);
%o A386918 (Magma) [2^n * Binomial(4*n,n): n in [0..26]]; // _Vincenzo Librandi_, Aug 11 2025
%Y A386918 Cf. A066381, A386919, A386920.
%Y A386918 Cf. A005810, A059304, A228484, A378804.
%K A386918 nonn,easy
%O A386918 0,2
%A A386918 _Seiichi Manyama_, Aug 08 2025