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A106823 Triangle read by rows: g.f. for row r is Product( (x^i-x^(r+1))/(1-x^i), i = 1..r-2).

%I A106823 #9 Sep 18 2021 03:52:46
%S A106823 1,1,1,0,1,1,1,1,0,0,0,1,1,2,2,2,1,1,0,0,0,0,0,0,1,1,2,3,3,3,3,2,1,1,
%T A106823 0,0,0,0,0,0,0,0,0,0,1,1,2,3,4,4,5,4,4,3,2,1,1,0,0,0,0,0,0,0,0,0,0,0,
%U A106823 0,0,0,0,1,1,2,3,4,5,6,6,6,6,5,4,3,2,1,1
%N A106823 Triangle read by rows: g.f. for row r is Product( (x^i-x^(r+1))/(1-x^i), i = 1..r-2).
%D A106823 See A008968 for references.
%H A106823 G. C. Greubel, <a href="/A106823/b106823.txt">Rows n = 0..25 of the irregular triangle, flattened</a>
%e A106823 Initial rows are:
%e A106823 [1]
%e A106823 [1]
%e A106823 [1]
%e A106823 [0, 1, 1, 1, 1]
%e A106823 [0, 0, 0, 1, 1, 2, 2, 2, 1, 1]
%e A106823 [0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1]
%e A106823 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1]
%p A106823 f3:=r->mul( (x^i-x^(r+1))/(1-x^i), i = 1..r-3); for r from 1 to 10 do series(f3(r),x,50); od:
%t A106823 f[n_, x_]:= Product[(x^j -x^(n+2))/(1-x^j), {j, n-2}];
%t A106823 T[n_]:= CoefficientList[f[n, x], x];
%t A106823 Table[T[n], {n, 0, 10}]//Flatten (* _G. C. Greubel_, Sep 14 2021 *)
%Y A106823 If the initial zeros in each row are omitted, we get A008968.
%Y A106823 Cf. A008967, A008968, A106822.
%K A106823 nonn,tabf
%O A106823 0,14
%A A106823 _N. J. A. Sloane_, May 20 2005