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A341372
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Regular triangle read by rows, T(n, k) is the number of cycles of length 2*k-1 of the permutation gamma on Dn, the set of Dyck words of length n, for n>=2 and 1<=k<=n-1.
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0
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2, 2, 1, 3, 2, 1, 3, 4, 4, 1, 4, 5, 11, 4, 1, 2, 10, 21, 14, 6, 1, 6, 10, 44, 34, 24, 6, 1, 5, 17, 67, 83, 74, 27, 8, 2, 4, 17, 119, 162, 212, 92, 44, 11, 1
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OFFSET
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2,1
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COMMENTS
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See the link for a description of the gamma permutation.
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LINKS
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Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Robert Cori, Some permutations on Dyck words, Theoretical Computer Science, Volume 635, 4 July 2016, Pages 51-63.
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EXAMPLE
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Triangle begins:
2;
2, 1;
3, 2, 1;
3, 4, 4, 1;
4, 5, 11, 4, 1;
2, 10, 21, 14, 6, 1;
6, 10, 44, 34, 24, 6, 1;
5, 17, 67, 83, 74, 27, 8, 2;
4, 17, 119, 162, 212, 92, 44, 11, 1;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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