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%I #10 Dec 29 2021 11:18:26
%S 1,1,0,1,1,0,1,2,1,0,1,3,4,0,0,1,4,9,6,0,0,1,5,16,24,10,0,0,1,6,25,58,
%T 66,14,0,0,1,7,36,118,212,174,20,0,0,1,8,49,208,560,758,462,20,0,0,1,
%U 9,64,334,1206,2620,2722,1178,22,0,0
%N Array read by antidiagonals: T(n,k) is the number of sequences of length n with terms in 1..k such that all Hankel matrices of an odd number of consecutive terms are invertible, n, k >= 0.
%C T(n,2) = 0 for n >= 15.
%C For a fixed k, what can be said about T(n,k) as n grows? (For k <= 2, T(n,k) = 0 for large n.)
%H Pontus von Brömssen, <a href="/A350364/b350364.txt">Antidiagonals n = 0..14, flattened</a>
%e Array begins:
%e n\k| 0 1 2 3 4 5 6 7
%e ---+-------------------------------------------
%e 0 | 1 1 1 1 1 1 1 1
%e 1 | 0 1 2 3 4 5 6 7
%e 2 | 0 1 4 9 16 25 36 49
%e 3 | 0 0 6 24 58 118 208 334
%e 4 | 0 0 10 66 212 560 1206 2282
%e 5 | 0 0 14 174 758 2620 6932 15506
%e 6 | 0 0 20 462 2722 12277 39871 105405
%e 7 | 0 0 20 1178 9628 57084 228451 714878
%e 8 | 0 0 22 3036 34132 265659 1309476 4849364
%Y Cf. A350330, A350365.
%Y Cf. A000012 (row n = 0), A001477 (row n = 1), A000290 (row n = 2), A000007 (column k = 0), A130716 (column k = 1).
%K nonn,tabl
%O 0,8
%A _Pontus von Brömssen_, Dec 27 2021