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A291954 Triangle read by rows: T(n,k) = T(n-k,k-1) - T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

%I A291954 #26 Sep 07 2017 09:07:35
%S A291954 1,0,1,0,-1,0,1,1,0,-1,-1,0,1,0,0,-1,0,1,0,1,1,-1,0,-1,-1,0,0,1,0,-1,
%T A291954 0,-1,0,2,1,0,1,1,-1,-1,0,-1,-1,1,0,0,1,0,-2,-1,0,-1,0,2,1,0,1,1,-2,0,
%U A291954 1,0,-1,-1,2,1,-1,0,1,0,-2,-1,0,0,-1,0,3,1,-1,0,1
%N A291954 Triangle read by rows: T(n,k) = T(n-k,k-1) - T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).
%H A291954 Seiichi Manyama, <a href="/A291954/b291954.txt">Rows n = 0..481, flattened</a>
%F A291954 G.f. of column k: x^(k*(k+1)/2) / Product_{j=1..k} (1+x^j).
%e A291954 First few rows are:
%e A291954   1;
%e A291954   0,  1;
%e A291954   0, -1;
%e A291954   0,  1,  1;
%e A291954   0, -1, -1;
%e A291954   0,  1,  0;
%e A291954   0, -1,  0,  1;
%e A291954   0,  1,  1, -1;
%e A291954   0, -1, -1,  0;
%e A291954   0,  1,  0, -1;
%e A291954   0, -1,  0,  2, 1.
%Y A291954 Row sums give A003406.
%Y A291954 Columns 0-1 give A000007, A062157.
%Y A291954 Cf. A008289, A291895, A291929.
%K A291954 sign,tabf
%O A291954 0,34
%A A291954 _Seiichi Manyama_, Sep 06 2017