|
%I #8 Oct 31 2017 08:58:06
%S 1,0,5,50,825,17500,458125,14268750,515440625,21188375000,
%T 976671703125,49893003906250,2797832158515625,170863509745312500,
%U 11287987223748828125,802119551344589843750,61005565392625400390625,4944614795517599218750000
%N 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 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 Inverse binomial transform of A008548. E.g.f.: exp(-x)/(1-5*x)^(1/5). - _Vladeta Jovovic_, Dec 17 2003
%F 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
%Y Cf. A000166, A053871, A033030, A088991.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 02 2003
|
