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Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,0,1,1,1,2,1,3,1,4,1,5,...], where DELTA is the operator defined in A084938.
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%I #11 Aug 24 2024 17:07:24

%S 1,0,1,0,1,1,0,1,3,1,0,1,6,7,1,0,1,10,24,16,1,0,1,15,60,86,40,1,0,1,

%T 21,125,301,312,116,1,0,1,28,231,826,1443,1215,395,1,0,1,36,392,1932,

%U 4992,7055,5187,1551,1,0,1,45,624,4032,14274,29629,36242,24280

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

%F Sum_{k>=0} T(n,k) = A000110(n).

%F T(n + 1; 2) = A000217(n).

%F T(n + 2; 3) = A014205(n)= (1/12)*(n + 5)*(n + 1)*n^2.

%F T(n + 2; n + 1) = A029761(n).

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 3, 1;

%e 0, 1, 6, 7, 1;

%e 0, 1, 10, 24, 16, 1; ....

%Y Cf. A084938, A085838.

%Y Cf. A000110, A000217, A014205, A029761.

%K easy,nonn,tabl

%O 0,9

%A _Philippe Deléham_, Jul 23 2003