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Triangle T(n,k), 0<= k <= n, read by rows; given by [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, ...] DELTA [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, ...] where DELTA is the operator defined in A084938.
2

%I #13 Jun 20 2023 10:08:44

%S 1,0,1,0,1,1,0,2,4,1,0,6,18,13,1,0,24,96,119,46,1,0,120,600,1059,777,

%T 199,1,0,720,4320,9890,10760,5536,1072,1,0,5040,35280,99158,142990,

%U 111316,44228,6985,1,0,40320,322560,1073692,1926312,2009578,1217352,395865,53218,1

%N Triangle T(n,k), 0<= k <= n, read by rows; given by [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, ...] DELTA [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, ...] where DELTA is the operator defined in A084938.

%F Sum_{k=0..n} T(n,k)*3^(n-k) = A128709(n). - _Philippe Deléham_, Mar 27 2007

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 2, 4, 1;

%e 0, 6, 18, 13, 1;

%e 0, 24, 96, 119, 46, 1;

%e ...

%Y Row sums: A094664.

%Y Columns: A000007, A000142, A001563.

%Y Diagonals: A000012, A014145.

%K nonn,tabl

%O 0,8

%A _Philippe Deléham_, Jun 02 2004

%E Row 9 completed by _Michel Marcus_, Jun 20 2023