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 A333310 Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j > sigma(j+1)/(j+1) for 1 <= j <= n-1. 2
 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1, 2, 2, 1, 3, 0, 1, 3, 5, 2, 3, 5, 0, 1, 3, 6, 5, 3, 4, 8, 0, 1, 4, 8, 12, 8, 5, 9, 13, 0, 1, 4, 12, 20, 18, 8, 11, 13, 21, 0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38, 0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS T(n+1,k+1) is equal to the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j >= sigma(j+1)/(j+1) for 1 <= j <= n-1. LINKS Seiichi Manyama, Rows n = 1..18, flattened Mathematics.StackExchange, Why are the numbers of two different permutations the same?, Mar 07 2020. EXAMPLE Triangle begins: n\k | 1 2 3 4 5 6 7 8 9 10 11 12 -----+-------------------------------------------- 1 | 1; 2 | 0, 1; 3 | 0, 1, 1; 4 | 0, 1, 1, 1; 5 | 0, 1, 2, 1, 2; 6 | 0, 1, 2, 2, 1, 3; 7 | 0, 1, 3, 5, 2, 3, 5; 8 | 0, 1, 3, 6, 5, 3, 4, 8; 9 | 0, 1, 4, 8, 12, 8, 5, 9, 13; 10 | 0, 1, 4, 12, 20, 18, 8, 11, 13, 21; 11 | 0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38; 12 | 0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64; CROSSREFS Row sums give A309807. Cf. A332954. Sequence in context: A114002 A114004 A306518 * A049986 A218797 A137289 Adjacent sequences: A333307 A333308 A333309 * A333311 A333312 A333313 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Mar 14 2020 STATUS approved

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Last modified March 20 14:05 EDT 2023. Contains 361383 sequences. (Running on oeis4.)