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 A383716 #36 Aug 04 2025 07:56:12
%S A383716 1,9,127,2001,33151,565249,9819391,172826369,3071424511,54992986113,
%T A383716 990477877247,17925526679553,325710362673151,5938147061596161,
%U A383716 108571788661555199,1990032340043366401,36554697970011340799,672749920475758460929,12402180156683794251775
%N A383716 a(n) = Sum_{k=0..n} binomial(4*n+1,k) * binomial(4*n-k,n-k).
%F A383716 a(n) = [x^n] (1+x)^(4*n+1)/(1-x)^(3*n+1).
%F A383716 a(n) = [x^n] 1/((1-x) * (1-2*x)^(3*n+1)).
%F A383716 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(4*n+1,k).
%F A383716 a(n) = Sum_{k=0..n} 2^k * binomial(3*n+k,k).
%o A383716 (PARI) a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(4*n-k, n-k));
%Y A383716 Cf. A178792, A383326.
%Y A383716 Cf. A370101.
%K A383716 nonn
%O A383716 0,2
%A A383716 _Seiichi Manyama_, Aug 04 2025