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A328650 Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1)/(1-x-2x^2).

%I A328650 #10 Nov 06 2019 19:16:49
%S A328650 -1,1,4,-3,-6,-12,5,24,24,32,-11,-50,-120,-80,-80,21,132,300,480,240,
%T A328650 192,-43,-294,-924,-1400,-1680,-672,-448,85,688,2352,4928,5600,5376,
%U A328650 1792,1024,-171,-1530,-6192,-14112,-22176,-20160,-16128,-4608,-2304,341,3420
%N A328650 Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1)/(1-x-2x^2).
%C A328650 It appears that the number of nonconstant polynomial divisors of the n-th polynomial is given by A032741.
%e A328650 First eight rows:
%e A328650     -1;
%e A328650      1,    4;
%e A328650      3,   -6,  -12;
%e A328650      5,   24,   24,    32;
%e A328650    -11,  -50, -120,   -80,   -80;
%e A328650     21,  132,  300,   480,   240,  192;
%e A328650    -43, -294, -924, -1400, -1680, -672, -448;
%e A328650     85,  688, 2352,  4928,  5600, 5376, 1792, 1024;
%e A328650 First eight polynomials:
%e A328650 -1
%e A328650 1 + 4 x
%e A328650 -3 (1 + 2 x + 4 x^2)
%e A328650 (1 + 4 x) (5 + 4 x + 8 x^2)
%e A328650 -11 - 50 x - 120 x^2 - 80 x^3 - 80 x^4
%e A328650 3 (1 + 4 x) (1 + 2 x + 4 x^2) (7 + 2 x + 4 x^2)
%e A328650 -43 - 294 x - 924 x^2 - 1400 x^3 - 1680 x^4 - 672 x^5 - 448 x^6
%e A328650 (1 + 4 x) (5 + 4 x + 8 x^2) (17 + 56 x + 120 x^2 + 32 x^3 + 32 x^4)
%t A328650 g[x_, n_] := Numerator[ Factor[D[1/(1 - x - 2 x^2), {x, n}]]]
%t A328650 Column[Expand[Table[g[x, n]/n!, {n, 0, 12}]]]  (* A328650 polynomials *)
%t A328650 h[n_] := CoefficientList[g[x, n]/n!, x];
%t A328650 Table[h[n], {n, 0, 10}] (* A328650 sequence *)
%t A328650 Column[%] (* A328650 array *)
%Y A328650 Cf. A000032, A328646.
%K A328650 tabl,sign
%O A328650 0,3
%A A328650 _Clark Kimberling_, Nov 01 2019