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 A066998 #28 Dec 09 2024 10:12:56
%S A066998 0,1,5,46,737,18426,663337,32503514,2080224897,168498216658,
%T A066998 16849821665801,2038828421561922,293591292704916769,
%U A066998 49616928467130933962,9724917979557663056553,2188106545400474187724426
%N A066998 a(0)=0; a(n) = n^2*a(n-1) + 1.
%C A066998 if s(n) is a sequence defined as s(0)=x, s(n) = n^2*s(n-1) + k, then s(n) = n!^2*x + a(n)*k. - _Gary Detlefs_, Feb 20 2010
%H A066998 Harry J. Smith, <a href="/A066998/b066998.txt">Table of n, a(n) for n = 0..100</a>
%H A066998 Alexandre Silva, Carlos Pereira dos Santos, João Pedro Neto, and Richard J. Nowakowski, <a href="https://doi.org/10.1016/j.tcs.2022.12.015">Disjunctive sums of quasi-nimbers</a>, Theor. Comp. Sci. (2022).
%F A066998 a(n) = (n!)^2*Sum_{i=1..n} 1/(i!)^2.
%F A066998 a(n) = floor((1-BesselI(0, 2))*(n!)^2). - _Benoit Cloitre_, Nov 02 2002
%F A066998 Sum_{n>=0} a(n) * x^n / (n!)^2 = (BesselI(0,2*sqrt(x)) - 1) / (1 - x). - _Ilya Gutkovskiy_, Jan 23 2021
%t A066998 RecurrenceTable[{a[0]==0,a[n]==n^2 a[n-1]+1},a,{n,20}] (* _Harvey P. Dale_, Jan 24 2019 *)
%o A066998 (PARI) a(n) = { my(a=0); for (n=1, n, a=n^2*a + 1); a } \\ _Harry J. Smith_, Apr 24 2010
%Y A066998 This is the same recurrence relation as A006040 except A006040 has a(0) = 1.
%K A066998 nonn
%O A066998 0,3
%A A066998 _Benoit Cloitre_, Jan 27 2002
%E A066998 Better description from _James D. Klein_, Feb 25 2002