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%I #12 Oct 10 2013 05:19:05
%S 1,0,4,32,432,7424,157120,3949056,114972928,3805503488,141137150976,
%T 5797706178560,261309106499584,12821127008550912,680286677982625792,
%U 38814037079505895424,2369659425449311272960,154142301601844298776576,10642813349855965483368448
%N Derangement numbers d(n,4) 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.
%H Vincenzo Librandi, <a href="/A088991/b088991.txt">Table of n, a(n) for n = 0..200</a>
%F Inverse binomial transform of A007696. E.g.f.: exp(-x)/(1-4*x)^(1/4). - _Vladeta Jovovic_, Dec 17 2003
%F a(n) ~ n^(n-1/4) * Gamma(3/4) * 4^n / (sqrt(Pi)*exp(n+1/4)). - _Vaclav Kotesovec_, Oct 08 2013
%t CoefficientList[Series[E^(-x)/(1-4*x)^(1/4), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 08 2013 *)
%Y Cf. A000166, A053871, A033030, A088992.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 02 2003