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 A387239 #22 Aug 27 2025 01:00:24
%S A387239 1,12,95,630,3801,21672,119154,639180,3369795,17543196,90476100,
%T A387239 463291920,2359240975,11961944400,60440659640,304543085040,
%U A387239 1531044995355,7682898791700,38494752520175,192632866196694,962948703201331,4809438625979592,24002988378037350,119719958370912900
%N A387239 a(n) = Sum_{k=0..n} binomial(n+3,k+3) * binomial(2*k+6,k+6).
%H A387239 Vincenzo Librandi, <a href="/A387239/b387239.txt">Table of n, a(n) for n = 0..500</a>
%F A387239 n*(n+6)*a(n) = (n+3) * (3*(2*n+5)*a(n-1) - 5*(n+2)*a(n-2)) for n > 1.
%F A387239 a(n) = Sum_{k=0..floor(n/2)} 3^(n-2*k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F A387239 a(n) = [x^n] (1+3*x+x^2)^(n+3).
%F A387239 E.g.f.: exp(3*x) * BesselI(3, 2*x), with offset 3.
%t A387239 Table[Sum[Binomial[n+3,k+3]* Binomial[2*k+6, k+6],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 24 2025 *)
%o A387239 (PARI) a(n) = sum(k=0, n, binomial(n+3, k+3)*binomial(2*k+6, k+6));
%o A387239 (Magma) [&+[Binomial(n+3,k+3) * Binomial(2*k+6,k+6): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 24 2025
%Y A387239 Cf. A026376, A026377.
%Y A387239 Cf. A126190.
%K A387239 nonn,new
%O A387239 0,2
%A A387239 _Seiichi Manyama_, Aug 23 2025