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 A387277 #15 Aug 30 2025 16:56:56
%S A387277 1,25,381,4585,47978,458010,4100370,35027850,288845370,2317794050,
%T A387277 18203687502,140533725150,1069904389008,8052575725680,60033791987424,
%U A387277 444015014417280,3261950250436845,23827019766988725,173193081555808545,1253583401573658925,9040278899072328006
%N A387277 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(n+4,k+4) * binomial(2*k+8,k+8).
%H A387277 Vincenzo Librandi, <a href="/A387277/b387277.txt">Table of n, a(n) for n = 0..800</a>
%F A387277 n*(n+8)*a(n) = (n+4) * (5*(2*n+7)*a(n-1) - 21*(n+3)*a(n-2)) for n > 1.
%F A387277 a(n) = Sum_{k=0..floor(n/2)} 5^(n-2*k) * binomial(n+4,n-2*k) * binomial(2*k+4,k).
%F A387277 a(n) = [x^n] (1+5*x+x^2)^(n+4).
%F A387277 E.g.f.: exp(5*x) * BesselI(4, 2*x), with offset 4.
%t A387277 Table[Sum[3^(n-k)*Binomial[n+4,k+4]*Binomial[2*k+8,k+8],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 30 2025 *)
%o A387277 (PARI) a(n) = sum(k=0, n, 3^(n-k)*binomial(n+4, k+4)*binomial(2*k+8, k+8));
%o A387277 (Magma) [&+[3^(n-k) * Binomial(n+4,k+4) * Binomial(2*k+8,k+8): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 30 2025
%Y A387277 Cf. A387275, A387276, A387278.
%Y A387277 Cf. A387274.
%K A387277 nonn,new
%O A387277 0,2
%A A387277 _Seiichi Manyama_, Aug 24 2025