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A136662 Number of cycles of the permutations of [1,2,...,n].

%I A136662 #24 Jan 26 2023 14:33:51
%S A136662 1,2,1,3,2,2,1,1,2,4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2,5,
%T A136662 4,4,3,3,4,4,3,3,2,2,3,3,2,4,3,3,2,2,3,3,4,2,3,4,3,3,2,2,3,3,2,2,1,1,
%U A136662 2,2,1,3,2,2,1,1,2,2,3,1,2,3,2,2,1,1,2,4,3,3,2,2,3,3,2,2,1,1,2,2,3,1,2,2,1
%N A136662 Number of cycles of the permutations of [1,2,...,n].
%C A136662 The row lengths sequence is A000142(n), n>=1, (factorials).
%C A136662 The permutations of [1,2,...,n] are ordered in the standard way (lexicographic or numerically increasing). E.g., in Maple as permute(n) list for not too large n (around 10).
%H A136662 Alois P. Heinz, <a href="/A136662/b136662.txt">Rows n = 1..8, flattened</a>
%H A136662 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000031">The number of cycles in the cycle decomposition of a permutation</a>
%H A136662 Wolfdieter Lang, <a href="/A136662/a136662.txt"> First rows and cycle decompositions</a>.
%F A136662 a(n,k) = number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.
%e A136662 Triangle begins:
%e A136662   [1];
%e A136662   [2,1];
%e A136662   [3,2,2,1,1,2];
%e A136662   [4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2];
%e A136662   ...
%e A136662 Row n=3: permutations of [1,2,3] in the order [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]. Cycle decomposition: [[[1], [2], [3]], [[1], [2, 3]], [[1, 2], [3]], [[1, 2, 3]], [[1, 3, 2]], [[1, 3], [2]]]. Number of cycles: [3,2,2,1,1,2], the entries of row n=3.
%Y A136662 Row sums (total cycle numbers) A000254.
%Y A136662 Cf. A130534.
%K A136662 nonn,easy,tabf
%O A136662 1,2
%A A136662 _Wolfdieter Lang_, Feb 22 2008, May 21 2008