Search: id:A055790
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%I A055790
%S A055790 0,2,4,14,64,362,2428,18806,165016,1616786,17487988,206918942,2657907184,
%T A055790 36828901754,547499510764,8691268384262,146725287298888,2624698909845026,
%U A055790 49592184973992676,986871395973226286,20630087248996393888,451982388752415571082
%N A055790 a(n) = n*a(n-1) + (n-2)*a(n-2) [a(0) = 0, a(1) = 2].
%C A055790 With offset 1, permanent of (0,1)-matrix of size n X (n+d) with d=1 and 
               n-1 zeros not on a line. This is a special case of Theorem 2.3 of 
               Seok-Zun Song et al. Extremes of permanents of (0,1)-matrices, p. 
               201-202. - Jaap Spies (j.spies(AT)hccnet.nl), Dec 12 2003
%C A055790 Number of degree-n permutations p such that p(i) != i+2 for each i=1,
               2,...,n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
%D A055790 Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, 
               Cambridge NY (1991), Chapter 7.
%D A055790 Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. 
               Algebra and its Applic. 373 (2003), p. 197-210.
%F A055790 a(n) = round[(n+3+1/n)*n!/e] = 2*A000153(n) = A000255(n-1)+A000255(n) 
               = A000166(n-1)+2*A000166(n)+A000166(n+1)
%e A055790 a(3) = 3*a(2)+(3-2)*a(1) = 12+2 = 14
%p A055790 f := proc(n) option remember; if n <= 1 then 2*n else n*f(n-1)+(n-2)*f(n-2); 
               fi; end;
%Y A055790 Cf. A000255, A000153, A000261, A001909, A001910, A090010, A090012-A090016.
%Y A055790 Apart from first term, appears in triangles A047920 or A068106 of differences 
               of factorials, i.e. as third term of A000142, A001563, A001564, A001565 
               etc.
%Y A055790 Sequence in context: A046911 A089127 A132852 this_sequence A020131 A032147 
               A007712
%Y A055790 Adjacent sequences: A055787 A055788 A055789 this_sequence A055791 A055792 
               A055793
%K A055790 nonn
%O A055790 0,2
%A A055790 Henry Bottomley (se16(AT)btinternet.com), Jul 13 2000

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