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Triangle read by rows: T(n,k) = (-1)^(k-1) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).
3

%I #15 Sep 08 2017 10:07:17

%S 1,0,1,0,1,0,1,-1,0,1,-1,0,1,-2,0,1,-2,-1,0,1,-3,-1,0,1,-3,-2,0,1,-4,

%T -3,0,1,-4,-4,1,0,1,-5,-5,1,0,1,-5,-7,2,0,1,-6,-8,3,0,1,-6,-10,5,0,1,

%U -7,-12,6,1,0,1,-7,-14,9,1,0,1,-8,-16,11,2,0,1,-8,-19

%N Triangle read by rows: T(n,k) = (-1)^(k-1) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

%H Seiichi Manyama, <a href="/A292049/b292049.txt">Rows n = 0..481, flattened</a>

%e First few rows are:

%e 1;

%e 0, 1;

%e 0, 1;

%e 0, 1, -1;

%e 0, 1, -1;

%e 0, 1, -2;

%e 0, 1, -2, -1;

%e 0, 1, -3, -1;

%e 0, 1, -3, -2;

%e 0, 1, -4, -3;

%e 0, 1, -4, -4, 1.

%Y Row sums give (-1)*A278400.

%Y Columns 0-1 give A000007, A000012.

%Y Cf. A292047.

%K sign,tabf,look

%O 0,14

%A _Seiichi Manyama_, Sep 08 2017