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Irregular triangle read by rows: T(n,k) = number of 1324-avoiding permutations of length n >= 0 having k >= 0 inversions.
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%I #16 Dec 27 2018 22:12:10

%S 1,1,1,1,1,2,2,1,1,2,5,6,5,3,1,1,2,5,10,16,20,20,15,9,4,1,1,2,5,10,20,

%T 32,51,67,79,80,68,49,29,14,5,1,1,2,5,10,20,36,61,96,148,208,268,321,

%U 351,347,308,241,165,98,49,20,6,1,1,2,5,10,20,36,65,106,171,262,397,568,784,1019,1264,1478,1628,1681,1619,1441,1173,866,574,338,174,76,27,7,1

%N Irregular triangle read by rows: T(n,k) = number of 1324-avoiding permutations of length n >= 0 having k >= 0 inversions.

%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 769, Fig. 12.13.

%e Triangle begins:

%e 1;

%e 1;

%e 1, 1;

%e 1, 2, 2, 1;

%e 1, 2, 5, 6, 5, 3, 1;

%e 1, 2, 5, 10, 16, 20, 20, 15, 9, 4, 1;

%e 1, 2, 5, 10, 20, 32, 51, 67, 79, 80, 68, 49, 29, 14, 5, 1;

%e ...

%Y The rows appear to be converging to A000712.

%Y Row sums are A061552.

%Y Cf. A188919.

%K nonn,tabf

%O 0,6

%A _N. J. A. Sloane_, Dec 25 2018

%E More terms from _Alois P. Heinz_, Dec 27 2018