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 A387310 #14 Aug 29 2025 17:47:37
%S A387310 1,21,330,4690,63690,844662,11052496,143462592,1852852365,23853938185,
%T A387310 306473670822,3932435239278,50417223635233,646085510253645,
%U A387310 8277409340709240,106037993391958936,1358437551566242347,17404555385537336583,223025734596708637750,2858460480570547144110
%N A387310 a(n) = Sum_{k=0..n} 3^k * binomial(n+2,k+2) * binomial(2*k+4,k+4).
%H A387310 Vincenzo Librandi, <a href="/A387310/b387310.txt">Table of n, a(n) for n = 0..800</a>
%F A387310 n*(n+4)*a(n) = (n+2) * (7*(2*n+3)*a(n-1) - 13*(n+1)*a(n-2)) for n > 1.
%F A387310 a(n) = Sum_{k=0..floor(n/2)} 9^k * 7^(n-2*k) * binomial(n+2,n-2*k) * binomial(2*k+2,k).
%F A387310 a(n) = [x^n] (1+7*x+9*x^2)^(n+2).
%F A387310 E.g.f.: exp(7*x) * BesselI(2, 6*x) / 9, with offset 2.
%t A387310 Table[Sum[3^k * Binomial[n+2,k+2]*Binomial[2*k+4, k+4],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 29 2025 *)
%o A387310 (PARI) a(n) = sum(k=0, n, 3^k*binomial(n+2, k+2)*binomial(2*k+4, k+4));
%o A387310 (Magma) [&+[3^k * Binomial(n+2,k+2) * Binomial(2*k+4,k+4): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 29 2025
%Y A387310 Cf. A387309, A387311.
%K A387310 nonn,new
%O A387310 0,2
%A A387310 _Seiichi Manyama_, Aug 25 2025