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%I #11 Sep 14 2021 17:34:32
%S 1,1,0,1,1,1,0,0,0,1,1,2,1,1,0,0,0,0,0,0,1,1,2,2,2,1,1,0,0,0,0,0,0,0,
%T 0,0,0,1,1,2,2,3,2,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,3,
%U 2,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,4,3,3,2,2,1
%N Triangle read by rows: g.f. for row r is Product_{i=1..r-2} (x^i-x^(r+1))/(1-x^i).
%D See A008967 for references.
%H G. C. Greubel, <a href="/A106822/b106822.txt">Rows n = 0..25 of the irregular triangle, flattened</a>
%e Initial rows are:
%e [1]
%e [1]
%e [0, 1, 1, 1]
%e [0, 0, 0, 1, 1, 2, 1, 1]
%e [0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1]
%e [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1]
%p f2:=r->mul( (x^i-x^(r+1))/(1-x^i), i = 1..r-2); for r from 1 to 10 do series(f2(r),x,50); od:
%t f[n_, x_]:= Product[(x^j - x^(n+2))/(1 - x^j), {j, n-1}];
%t T[n_]:= CoefficientList[f[n, x], x];
%t Table[T[n], {n, 0, 10}]//Flatten (* _G. C. Greubel_, Sep 12 2021 *)
%o (PARI) row(r) = Vecrev(prod(i=1, r-2, (x^i-x^(r+1))/(1-x^i))); \\ _Michel Marcus_, Sep 14 2021
%Y If the initial zeros in each row are omitted, we get A008967.
%Y Cf. A008967, A106823.
%K nonn,tabf
%O 0,12
%A _N. J. A. Sloane_, May 20 2005
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