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A261763 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.

%I A261763 #18 Oct 31 2015 15:33:32
%S A261763 1,1,2,1,4,7,1,8,26,34,1,16,115,179,209,1,32,542,1102,1402,1546,1,64,
%T A261763 2809,7609,10759,12487,13327,1,128,15374,56534,92234,113402,125162,
%U A261763 130922,1,256,89737,457993,865393,1139569,1304209,1396369,1441729
%N A261763 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.
%D A261763 A. Laradji and A. Umar, On the number of subpermutations with fixed orbit size, Ars Combinatoria, 109 (2013), 447-460.
%F A261763 T(n,n) = A002720(n).
%F A261763 T(n,k) = Sum_{i=0..n} binomial(n,i)*A261762(n-i,k).
%F A261763 E.g.f. of column k: exp(Sum_{j=1..k} (j+1)*x^j/j).
%e A261763 T(3, 2) = 26 because there are 26 subpermutations on {1,2,3}, each of whose orbit is of size at most 2, namely:
%e A261763 Empty map, 1-->1, 1-->2, 1-->3, 2-->1, 2-->2, 2-->3, 3-->1, 3-->2, 3-->3, (1,2) --> (1,2), (1,3) --> (1,3), (2,3) --> (2,3), (1,2) --> (2,1), (1,3) --> (3,1), (2,3) --> (3,2), (1,2) --> (1,3), (1,3) --> (1,2), (2,3) --> (2,1), (1,2) --> (3,2), (1,3) --> (2,3), (2,3) --> (1,3), (1,2,3) --> (1,3,2), (1,2,3) --> (3,2,1), (1,2,3) --> (2,1,3), (1,2,3) --> (1,2,3).
%e A261763 Triangle starts:
%e A261763 1;
%e A261763 1, 2;
%e A261763 1, 4, 7;
%e A261763 1, 8, 26, 34;
%e A261763 1, 16, 115, 179, 209;
%e A261763 ...
%Y A261763 Cf. A157400, A261762, A261764, A261765, A261766, A261767.
%K A261763 nonn,tabl
%O A261763 0,3
%A A261763 _Samira Stitou_, Sep 21 2015
%E A261763 More terms from _Alois P. Heinz_, Oct 07 2015