%I A033030
%S A033030 1,0,3,18,189,2484,40095,766422,16936857,424878696,11929019931,370616958810,
%T A033030 12624017298453,467806833261468,18736803171836919,806593620214132254,37139869052368612785,
%U A033030 1821430208283971761872,94787073944153359107507,5216859224231615866946466
%N A033030 Derangement numbers d(n,3) 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.
%F A033030 Inverse binomial transform of A007559. E.g.f.: exp(-x)/(1-3*x)^(1/3). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 17 2003
%p A033030 k := 3; d := proc(n) global k; option remember; if n = 0 then RETURN(1) 
               end if; if n = 1 then RETURN(0) end if; k*(n - 1)*(d(n - 1) + d(n 
               - 2)) end proc;
%Y A033030 d(n, 1) gives A000166, d(n, 2) gives A053871, d(n, 4) gives A088991, 
               d(n, 5) gives A088992.
%Y A033030 Sequence in context: A132853 A084879 A141118 this_sequence A002824 A160707 
               A135077
%Y A033030 Adjacent sequences: A033027 A033028 A033029 this_sequence A033031 A033032 
               A033033
%K A033030 nonn,easy
%O A033030 0,3
%A A033030 N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2003