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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 September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)