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A106822 Triangle read by rows: g.f. for row r is Product_{i=1..r-2} (x^i-x^(r+1))/(1-x^i).

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