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%I #6 Dec 04 2016 19:46:26
%S 2,1,2,1,3,2,1,6,11,6,1,24,191,564,396,1,1176,435503,52853928,
%T 1076228496,1023808896,1,2153328000,1213787658541781999,
%U 58766849935745220643571376,25431652043775702966453113185344,29851714119640536870115136698893312
%N Self-generating triangle based on symmetric functions.
%C Let row n+1 be (c0, c1, c2,...,cn). Then
%C c0*x^n + c1*x^(n-1) +...+ cn=(x+b0)(x+b1)...(x+bm),
%C where (b0,b1,b2,...,bm) is row n.
%F row n+1 : f(0,r), f(1,r),...f(n,r), where f(k,r)=(k-th elementary symmetric function), r=(row n).
%e First five rows:
%e 2
%e 1....2
%e 1....3......2
%e 1....6......11......6
%e 1....24....191....564....396
%e The factorization property is illustrated by
%e x^2 + 3x + 2 -> (x+1)(x+3)(x+2) = x^3 + 6x^2 + 11x + 6.
%t s =.; s[1] = {2};
%t Prepend[Table[s[z] = Table[SymmetricPolynomial
%t [k, s[z - 1]], {k, 0, z - 1}], {z, 2, 7}], s[1]]
%t % // TableForm (* A203301 triangle *)
%t %% // Flatten (* A203301 sequence *)
%t (* _Peter J. C. Moses_, Dec 30 2011 *)
%Y Cf. A203300.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Dec 31 2011
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