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 A089466 #36 Jan 12 2025 23:57:05
%S A089466 1,1,3,18,163,1950,28821,505876,10270569,236644092,6098971555,
%T A089466 173823708696,5427760272507,184267682837992,6757353631762293,
%U A089466 266191329601854000,11210291102456374801,502602430218071545104,23900770928782913595651,1201581698963550283673632
%N A089466 Inverse hyperbinomial transform of A089467.
%C A089466 See A088956 for the definition of the hyperbinomial transform.
%C A089466 a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the functional digraph contains no cycles of length 2. - _Geoffrey Critzer_, Mar 21 2012
%H A089466 Vincenzo Librandi, <a href="/A089466/b089466.txt">Table of n, a(n) for n = 0..100</a>
%F A089466 A089467(n) = Sum_{k=0..n} (n-k+1)^(n-k-1)*C(n, k)*a(k).
%F A089466 a(n) = Sum_{m=0..n} (Sum_{j=0..m} C(m, j)*C(n, n-m-j)*(n-1)^(n-m-j)*(m+j)!/(-2)^j)/m!.
%F A089466 E.g.f.: exp(-(T(x))^2/2)/(1-T(x)), where T(x) is the e.g.f. for A000169. - _Geoffrey Critzer_, Mar 21 2012
%F A089466 a(n) ~ exp(-1/2) * n^n. - _Vaclav Kotesovec_, Oct 08 2013
%F A089466 a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * n^(n - 2*k) / (k! * (n - 2*k)!). - _Daniel Suteu_, Jun 19 2018
%t A089466 nn=20; t=Sum[n^(n-1)x^n/n!,{n,1,nn}]; a=Log[1/(1-t)]; Range[0,nn]! CoefficientList[Series[Exp[a-t^2/2], {x,0,nn}], x] (* _Geoffrey Critzer_, Mar 21 2012 *)
%o A089466 (PARI) a(n)=if(n<0,0,sum(m=0,n,sum(j=0,m,binomial(m,j)*binomial(n,n-m-j)*(n-1)^(n-m-j)*(m+j)!/(-2)^j)/m!))
%o A089466 (PARI) a(n) = n! * sum(k=0, n\2, (-1/2)^k * n^(n - 2*k) / (k! * (n - 2*k)!)); \\ _Daniel Suteu_, Jun 19 2018
%Y A089466 Cf. A089467, A088956.
%K A089466 nonn
%O A089466 0,3
%A A089466 _Paul D. Hanna_, Nov 08 2003