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 A387338 #18 Aug 29 2025 14:34:22
%S A387338 1,12,100,720,4809,30744,191184,1167120,7033785,41999364,249075684,
%T A387338 1469561184,8636441905,50600529840,295755641152,1725379046496,
%U A387338 10050215851665,58470232877820,339832224226180,1973538115293360,11453616812552761,66436765880135112
%N A387338 a(n) = Sum_{k=0..n} 2^k * binomial(n+3,k) * binomial(n+3,k+3).
%H A387338 Vincenzo Librandi, <a href="/A387338/b387338.txt">Table of n, a(n) for n = 0..800</a>
%F A387338 n*(n+6)*a(n) = (n+3) * (3*(2*n+5)*a(n-1) - (n+2)*a(n-2)) for n > 1.
%F A387338 a(n) = Sum_{k=0..floor(n/2)} 2^k * 3^(n-2*k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F A387338 a(n) = [x^n] (1+3*x+2*x^2)^(n+3).
%F A387338 E.g.f.: exp(3*x) * BesselI(3, 2*sqrt(2)*x) / (2*sqrt(2)), with offset 3.
%t A387338 Table[Sum[2^k * Binomial[n+3,k]*Binomial[n+3, k+3],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 29 2025 *)
%o A387338 (PARI) a(n) = sum(k=0, n, 2^k*binomial(n+3, k)*binomial(n+3, k+3));
%o A387338 (Magma) [&+[2^k * Binomial(n+3,k) * Binomial(n+3,k+3): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 29 2025
%Y A387338 Cf. A002696, A387339.
%Y A387338 Cf. A387342.
%K A387338 nonn,new
%O A387338 0,2
%A A387338 _Seiichi Manyama_, Aug 27 2025