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A327316 Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: p(x,n) = ((x+r)^n - (x+s)^n)/(r - s), where r = 3 and s = 2.

%I A327316 #12 Nov 07 2019 04:24:55
%S A327316 1,5,2,19,15,3,65,76,30,4,211,325,190,50,5,665,1266,975,380,75,6,2059,
%T A327316 4655,4431,2275,665,105,7,6305,16472,18620,11816,4550,1064,140,8,
%U A327316 19171,56745,74124,55860,26586,8190,1596,180,9,58025,191710,283725,247080
%N A327316 Triangular array read by rows: row n shows the coefficients of this polynomial of degree n:  p(x,n) = ((x+r)^n - (x+s)^n)/(r - s), where r = 3 and s = 2.
%C A327316 For every choice of integers r and s, the polynomials p(n,x) form a strong divisibility sequence. Thus, if r, s, and x are integers, then p(x,n) is a strong divisibility sequence.  That is, gcd(p(x,h),p(x,k)) = p(x,gcd(h,k)).
%e A327316 First seven rows:
%e A327316      1
%e A327316      5      2
%e A327316     19     15     3
%e A327316     65     76    30     4
%e A327316    211    325   190    50    5
%e A327316    665   1266   975   380   75    6
%e A327316   2059   4655  4431  2275  665  105   7
%t A327316 f[x_, n_] := ((x + r)^n - (x + s)^n)/(r - s);
%t A327316 r = 3; s = 2;
%t A327316 Column[Table[Expand[f[x, n]], {n, 1, 5}]]
%t A327316 c[x_, n_] := CoefficientList[Expand[f[x, n]], x]
%t A327316 TableForm[Table[c[x, n], {n, 1, 10}]] (* A327316 array *)
%t A327316 Flatten[Table[c[x, n], {n, 1, 12}]]   (* A327316 sequence *)
%Y A327316 Cf. A001047 (x=0), A005061 (x=1), A005060 (x=2), A005062 (x=3), A081200 (x=1/2).
%K A327316 nonn,tabl
%O A327316 1,2
%A A327316 _Clark Kimberling_, Nov 01 2019