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 A180255 #29 Jun 19 2025 11:50:37
%S A180255 0,1,6,57,916,22905,824586,40404721,2585902152,209458074321,
%T A180255 20945807432110,2534442699285321,364959748697086236,
%U A180255 61678197529807573897,12088926715842284483826,2720008511064514008860865,696322178832515586268381456,201237109682597004431562240801
%N A180255 a(n) = n^2 * a(n-1) + n, a(0)=0.
%C A180255 Integral_{x=0..1} x^n*BesselI(0,2*x^(1/2)) dx = A006040(n)*BesselI(1,2) - a(n)*BesselI(0,2). An elementary consequence is the irrationality of BesselI(0,2)/BesselI(1,2).
%H A180255 Paolo Xausa, <a href="/A180255/b180255.txt">Table of n, a(n) for n = 0..250</a> (terms 0..41 from Vincenzo Librandi)
%F A180255 From _Seiichi Manyama_, Jan 05 2024: (Start)
%F A180255 a(n) = (n!)^2 * Sum_{k=0..n} k/(k!)^2.
%F A180255 a(n) = n * A228229(n-1) for n > 0. (End)
%t A180255 FoldList[#2^2*# + #2 &, Range[0, 20]] (* _Paolo Xausa_, Jun 19 2025 *)
%o A180255 (PARI)
%o A180255 a(n)=if(n==0,0,(n)^2*a(n-1)+(n));
%o A180255 for(n=0,12,print1(a(n),", ")); /* show terms */
%o A180255 (Maxima) a[0]:0$ a[n]:=n^2*a[n-1]+n$ makelist(a[n], n, 0, 15); /* _Bruno Berselli_, May 23 2011 */
%Y A180255 Cf. A006040, A007526, A066998, A228229.
%K A180255 nonn
%O A180255 0,3
%A A180255 _Groux Roland_, Jan 17 2011