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 A136662 Number of cycles of the permutations of [1,2,...,n]. 3
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The row lengths sequence is A000142(n), n>=1, (factorials). 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). LINKS Alois P. Heinz, Rows n = 1..8, flattened FindStat - Combinatorial Statistic Finder, The number of cycles in the cycle decomposition of a permutation Wolfdieter Lang, First rows and cycle decompositions. FORMULA a(n,k) = number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order. EXAMPLE Triangle begins: [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]; ... 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. CROSSREFS Row sums (total cycle numbers) A000254. Cf. A130534. Sequence in context: A290536 A352570 A277855 * A023595 A177718 A057515 Adjacent sequences: A136659 A136660 A136661 * A136663 A136664 A136665 KEYWORD nonn,easy,tabf AUTHOR Wolfdieter Lang, Feb 22 2008, May 21 2008 STATUS approved

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Last modified December 4 10:17 EST 2023. Contains 367560 sequences. (Running on oeis4.)