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 A216831 #28 Jun 19 2022 08:29:08
%S A216831 1,2,11,88,905,11246,162607,2668436,48830273,983353690,21570885011,
%T A216831 511212091952,13001401709881,352856328962918,10170853073795975,
%U A216831 310093415465876716,9964607161173899777,336439048405066012466,11902368222382731461083,440122520333417057761160
%N A216831 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k!.
%H A216831 Vincenzo Librandi, <a href="/A216831/b216831.txt">Table of n, a(n) for n = 0..200</a>
%F A216831 Recurrence: (8*n^2+31*n+21)*a(n+3) - (24*n^3+157*n^2+308*n+162)*a(n+2) + (24*n^4+117*n^3+178*n^2+71*n-18)*a(n+1) - (8*n^2+31*n+30)*(n+1)^3*a(n) = 0.
%F A216831 a(n) ~ n^(n-1/6)/(sqrt(6*Pi)*exp(n+n^(1/3)-3*n^(2/3)-1/3)). - _Vaclav Kotesovec_, Sep 30 2012
%F A216831 a(n) = hypergeom([-n, -n, -n], [1], -1). - _Vladimir Reshetnikov_, Sep 28 2016
%F A216831 a(n) = Sum_{k=0..n} binomial(n, k)*|A021009(n, k)|. - _Peter Luschny_, May 04 2021
%F A216831 Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} x^n / n!^3. - _Ilya Gutkovskiy_, Jun 19 2022
%t A216831 Table[Sum[Binomial[n, k]^3*k!, {k, 0, n}], {n, 0, 25}]
%t A216831 Table[HypergeometricPFQ[{-n, -n, -n}, {1}, -1], {n, 0, 20}] (* _Vladimir Reshetnikov_, Sep 28 2016 *)
%o A216831 (PARI) a(n) = sum(k=0, n, binomial(n,k)^3 * k!); \\ _Michel Marcus_, May 04 2021
%Y A216831 Cf. A000522, A002720, A000172, A119400, A206178, A021009.
%K A216831 nonn
%O A216831 0,2
%A A216831 _Vaclav Kotesovec_, Sep 17 2012