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A136662 Number of cycles of the permutations of [1,2,...,n], for n=1,2,3,... 3

%I

%S 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 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 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 Number of cycles of the permutations of [1,2,...,n], for n=1,2,3,...

%C The row lengths sequence is A000142(n), n>=1, (factorials).

%C 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 Alois P. Heinz, <a href="/A136662/b136662.txt">Rows n = 1..8, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000031">The number of cycles in the cycle decomposition of a permutation</a>

%H W. Lang, <a href="/A136662/a136662.txt"> First rows and cycle decompositions</a>.

%F a(n,k)= number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.

%e [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];...

%e 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], the entries of row n=3.

%Y Row sums (total cycle numbers) A000254.

%Y Cf. A130534.

%K nonn,easy,tabf

%O 1,2

%A _Wolfdieter Lang_, Feb 22 2008, May 21 2008

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)