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 A387311 #16 Aug 30 2025 10:25:55
%S A387311 1,28,535,8750,132041,1900808,26557986,363716220,4912064355,
%T A387311 65673861484,871539802276,11501122783696,151118588963615,
%U A387311 1978948331160080,25846338449608184,336857447941007280,4382848524348689883,56947000383926523780,739095412895790074215,9583718189242229830798
%N A387311 a(n) = Sum_{k=0..n} 3^k * binomial(n+3,k+3) * binomial(2*k+6,k+6).
%H A387311 Vincenzo Librandi, <a href="/A387311/b387311.txt">Table of n, a(n) for n = 0..800</a>
%F A387311 n*(n+6)*a(n) = (n+3) * (7*(2*n+5)*a(n-1) - 13*(n+2)*a(n-2)) for n > 1.
%F A387311 a(n) = Sum_{k=0..floor(n/2)} 9^k * 7^(n-2*k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F A387311 a(n) = [x^n] (1+7*x+9*x^2)^(n+3).
%F A387311 E.g.f.: exp(7*x) * BesselI(3, 6*x) / 27, with offset 3.
%t A387311 Table[Sum[3^k * Binomial[n+3,k+3]*Binomial[2*k+6, k+6],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 29 2025 *)
%o A387311 (PARI) a(n) = sum(k=0, n, 3^k*binomial(n+3, k+3)*binomial(2*k+6, k+6));
%o A387311 (Magma) [&+[3^k * Binomial(n+3,k+3) * Binomial(2*k+6,k+6): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 29 2025
%Y A387311 Cf. A387309, A387310.
%K A387311 nonn,new
%O A387311 0,2
%A A387311 _Seiichi Manyama_, Aug 25 2025