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 A119401 #16 Jul 11 2025 16:40:30
%S A119401 1,0,-3,46,-927,25476,-922715,42240402,-2337537279,147901509928,
%T A119401 -9689806983699,464655683171670,44744831894861857,
%U A119401 -27559636076854374804,9449663596631181414933,-3046842389019074859527174,1013788651063121586526459905
%N A119401 a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n,k).
%F A119401 Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1+x)))/(1+x).
%F A119401 a(n) = -3*(n-1)*n*a(n-1) - 3*(n-1)^4*a(n-2) - (n-2)^3*(n-1)^3*a(n-3). - _Vaclav Kotesovec_, Jun 08 2019
%F A119401 a(n) = Sum_{k=0..n} (-1)^k*(k!)^2*binomial(n,k)^3. - _Ridouane Oudra_, Jul 11 2025
%t A119401 Table[Sum[(-1)^(n - k)*(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] (* _Stefan Steinerberger_, Jun 17 2007 *)
%Y A119401 Cf. A119400.
%K A119401 easy,sign
%O A119401 0,3
%A A119401 _Vladeta Jovovic_, Jul 25 2006
%E A119401 More terms from _Stefan Steinerberger_, Jun 17 2007