cp's OEIS Frontend

A332954 Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(j)/(j+k) > sigma(j+1)/(j+k+1) for 1 <= j <= n-1.

%I A332954 #24 Mar 15 2020 02:49:34
%S A332954 1,1,1,1,1,1,2,1,1,1,3,2,1,1,1,6,3,2,1,1,1,9,5,3,2,1,1,1,19,8,5,3,2,1,
%T A332954 1,1,30,13,7,5,3,2,1,1,1,60,21,12,7,5,3,2,1,1,1,108,38,17,11,7,5,3,2,
%U A332954 1,1,1
%N A332954 Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(j)/(j+k) > sigma(j+1)/(j+k+1) for 1 <= j <= n-1.
%C A332954 Conjecture: T(2*n+4,n) = A052955(n+2). This is true for n <= 10.
%C A332954 T(n+1,k) is equal to the number of permutations sigma of [n] such that sigma(j)/(j+k) >= sigma(j+1)/(j+k+1) for 1 <= j <= n-1.
%H A332954 Seiichi Manyama, <a href="/A332954/b332954.txt">Rows n = 0..18, flattened</a>
%H A332954 Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/3572301/why-are-the-numbers-of-two-different-permutations-the-same">Why are the numbers of two different permutations the same?</a>, Mar 07 2020.
%e A332954 Triangle begins:
%e A332954 n\k  |   0   1   2   3   4  5  6  7  8  9 10 11
%e A332954 -----+-----------------------------------------
%e A332954    0 |   1;
%e A332954    1 |   1,  1;
%e A332954    2 |   1,  1,  1;
%e A332954    3 |   2,  1,  1,  1;
%e A332954    4 |   3,  2,  1,  1,  1;
%e A332954    5 |   6,  3,  2,  1,  1, 1;
%e A332954    6 |   9,  5,  3,  2,  1, 1, 1;
%e A332954    7 |  19,  8,  5,  3,  2, 1, 1, 1;
%e A332954    8 |  30, 13,  7,  5,  3, 2, 1, 1, 1;
%e A332954    9 |  60, 21, 12,  7,  5, 3, 2, 1, 1, 1;
%e A332954   10 | 108, 38, 17, 11,  7, 5, 3, 2, 1, 1, 1;
%e A332954   11 | 222, 64, 31, 16, 11, 7, 5, 3, 2, 1, 1, 1;
%Y A332954 T(n,0) gives A309807.
%Y A332954 Cf. A052955.
%K A332954 nonn,tabl
%O A332954 0,7
%A A332954 _Seiichi Manyama_, Mar 04 2020