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%I #18 Nov 17 2015 03:59:06
%S 1,0,3,8,30,144,840,5760,45360,403200,3991680,43545600,518918400,
%T 6706022400,93405312000,1394852659200,22230464256000,376610217984000,
%U 6758061133824000,128047474114560000,2554547108585472000,53523844179886080000,1175091669949317120000
%N a(n) is the number of partial derangements of an n-set with at least one orbit of size exactly n.
%D A. Laradji and A. Umar, On the number of subpermutations with fixed orbit size, Ars Combinatoria, 109 (2013), 447-460.
%F a(n) = A261765(n,n) - A261765(n,n-1) for n>0, a(0)=1.
%e a(3) = 8 because there are 8 partial derangements on {1,2,3} with at least one orbit of size 3 namely: (1,2) --> (2,3), (1,2) --> (3,1), (1,3) --> (2,1), (1,3) --> (3,2), (2,3) --> (3,1), (2,3) --> (1,2), (1,2,3) --> (2,3,1), (1,2,3) --> (3,1,2).
%Y Cf. A001048, A059171, A157400, A261762, A261763, A261764, A261765, A261767.
%K nonn
%O 0,3
%A _Samira Stitou_, Sep 21 2015
%E More terms from _Alois P. Heinz_, Nov 04 2015