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 A387274 #15 Aug 31 2025 10:30:14
%S A387274 1,20,246,2408,20636,162288,1203000,8546208,58823919,395245708,
%T A387274 2606333730,16933021560,108703640136,691068080928,4358220121296,
%U A387274 27301946599872,170074452183570,1054434358722024,6510869338671852,40063301434583504,245781459952640040
%N A387274 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(n+4,k+4) * binomial(2*k+8,k+8).
%H A387274 Vincenzo Librandi, <a href="/A387274/b387274.txt">Table of n, a(n) for n = 0..800</a>
%F A387274 n*(n+8)*a(n) = (n+4) * (4*(2*n+7)*a(n-1) - 12*(n+3)*a(n-2)) for n > 1.
%F A387274 a(n) = Sum_{k=0..floor(n/2)} 4^(n-2*k) * binomial(n+4,n-2*k) * binomial(2*k+4,k).
%F A387274 a(n) = [x^n] (1+4*x+x^2)^(n+4).
%F A387274 E.g.f.: exp(4*x) * BesselI(4, 2*x), with offset 4.
%t A387274 Table[Sum[2^(n-k)*Binomial[n+4,k+4]*Binomial[2*k+8,k+8],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 31 2025 *)
%o A387274 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(n+4, k+4)*binomial(2*k+8, k+8));
%o A387274 (Magma) [&+[2^(n-k) * Binomial(n+4,k+4) * Binomial(2*k+8,k+8): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 31 2025
%Y A387274 Cf. A344055, A387272, A387273.
%K A387274 nonn,new
%O A387274 0,2
%A A387274 _Seiichi Manyama_, Aug 24 2025