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 A354944 #7 Jun 19 2022 08:29:31
%S A354944 1,0,-10,60,1560,-39880,-491760,45672060,-155935360,-77656158000,
%T A354944 2116774828800,166585352850620,-11925674437248000,-330617542587341880,
%U A354944 69148933431781898240,-543549949643024194500,-434534462104188331130880,21521903478880966780355360
%N A354944 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-n)^(n-k).
%F A354944 a(n) = n!^3 * [x^n] BesselI(0,2*sqrt(x)) * Sum_{k>=0} (-n)^k * x^k / k!^3.
%t A354944 Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k]^3 k! (-n)^(n - k), {k, 0, n}], {n, 0, 17}]
%t A354944 Unprotect[Power]; 0^0 = 1; Table[n!^3 SeriesCoefficient[BesselI[0, 2 Sqrt[x]] Sum[(-n)^k x^k/k!^3, {k, 0, n}], {x, 0, n}], {n, 0, 17}]
%o A354944 (PARI) a(n) = sum(k=0, n, binomial(n,k)^3 * k! * (-n)^(n-k)); \\ _Michel Marcus_, Jun 12 2022
%Y A354944 Cf. A134095, A277423, A336180, A343840, A354941, A354942, A354943.
%K A354944 sign
%O A354944 0,3
%A A354944 _Ilya Gutkovskiy_, Jun 12 2022