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 A088992 #13 Apr 24 2025 09:44:45
%S A088992 1,0,5,50,825,17500,458125,14268750,515440625,21188375000,
%T A088992 976671703125,49893003906250,2797832158515625,170863509745312500,
%U A088992 11287987223748828125,802119551344589843750,61005565392625400390625,4944614795517599218750000
%N A088992 Derangement numbers d(n,5) where d(n,k) = k(n-1)(d(n-1,k) + d(n-2,k)), with d(0,k) = 1 and d(1,k) = 0.
%C A088992 In general, d(n,k) is asymptotic to sqrt(2*Pi) * k^n * n^(n + 1/2) / (Gamma(1/k) * exp((n*k+1)/k) * n^((k-1)/k)), for k>0. - _Vaclav Kotesovec_, Oct 31 2017
%F A088992 Inverse binomial transform of A008548. E.g.f.: exp(-x)/(1-5*x)^(1/5). - _Vladeta Jovovic_, Dec 17 2003
%F A088992 a(n) ~ Pi * sqrt(2) * n^(n-3/10) * 5^n / (sqrt(Pi) * Gamma(1/5) * exp(n + 1/5)). - _Vaclav Kotesovec_, Oct 31 2017
%F A088992 a(n) = (-1)^n * n! * Sum_{k=0..n} 5^k * binomial(-1/5,k)/(n-k)!. - _Seiichi Manyama_, Apr 23 2025
%Y A088992 Cf. A000166, A053871, A033030, A088991.
%K A088992 nonn,easy
%O A088992 0,3
%A A088992 _N. J. A. Sloane_, Nov 02 2003