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A261767 Triangle read by rows: T(n,k) is the number of subpermutations of an n-set, whose orbits are each of size at most k with at least one orbit of size exactly k.

%I A261767 #18 Oct 31 2015 15:36:07
%S A261767 1,1,1,1,3,3,1,7,18,8,1,15,99,64,30,1,31,510,560,300,144,1,63,2745,
%T A261767 4800,3150,1728,840
%N A261767 Triangle read by rows: T(n,k) is the number of subpermutations of an n-set, whose orbits are each of size at most k with at least one orbit of size exactly k.
%D A261767 A. Laradji and A. Umar, On the number of subpermutations with fixed orbit size, Ars Combinatoria, 109 (2013), 447-460.
%F A261767 T(n, k) = A261763(n, k) - A261763(n, k-1), T(n, n) = A261766(n) for all n not equal to 1 and T(1, 1) = 1.
%e A261767 T(3, 2) = 18 because there are 18 subpermutations on {1,2,3} whose orbits are each of size at most 2 with at least one orbit of size exactly 2, namely: (1 2 --> 2 1), (1 3 --> 3 1), (2 3 --> 3 2), (123 --> 213), (123 --> 321), (123 --> 132); (1-->2), (1-->3), (2-->1), (2-->3), (3-->1), (3-->2); (13-->23), (12-->32), (23-->13), (32-->33), (23-->21), (13-->12).
%e A261767 Triangle starts:
%e A261767 1;
%e A261767 1, 1;
%e A261767 1, 3, 3;
%e A261767 1, 7, 18, 8;
%e A261767 1, 15, 99, 64, 30;
%e A261767 1, 31, 510, 560, 300, 144;
%e A261767 ...
%Y A261767 Cf. A261762, A261763, A261764, A261765, A261766, A261767.
%Y A261767 Row sums give A002720.
%K A261767 nonn,tabl,more
%O A261767 0,5
%A A261767 _Samira Stitou_, Sep 21 2015