A106823 - OEIS

%I #9 Sep 18 2021 03:52:46

%S 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 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 0,0,0,0,1,1,2,3,4,5,6,6,6,6,5,4,3,2,1,1

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

%D See A008968 for references.

%H G. C. Greubel, <a href="/A106823/b106823.txt">Rows n = 0..25 of the irregular triangle, flattened</a>

%e Initial rows are:

%e [1]

%e [1]

%e [1]

%e [0, 1, 1, 1, 1]

%e [0, 0, 0, 1, 1, 2, 2, 2, 1, 1]

%e [0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1]

%e [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1]

%p 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 f[n_, x_]:= Product[(x^j -x^(n+2))/(1-x^j), {j, n-2}];

%t T[n_]:= CoefficientList[f[n, x], x];

%t Table[T[n], {n, 0, 10}]//Flatten (* _G. C. Greubel_, Sep 14 2021 *)

%Y If the initial zeros in each row are omitted, we get A008968.

%Y Cf. A008967, A008968, A106822.

%K nonn,tabf

%O 0,14

%A _N. J. A. Sloane_, May 20 2005