A203301 Self-generating triangle based on symmetric functions.

2, 1, 2, 1, 3, 2, 1, 6, 11, 6, 1, 24, 191, 564, 396, 1, 1176, 435503, 52853928, 1076228496, 1023808896, 1, 2153328000, 1213787658541781999, 58766849935745220643571376, 25431652043775702966453113185344, 29851714119640536870115136698893312

Offset

1,1

Comments

Let row n+1 be (c0, c1, c2,...,cn). Then

c0*x^n + c1*x^(n-1) +...+ cn=(x+b0)(x+b1)...(x+bm),

where (b0,b1,b2,...,bm) is row n.

Links

Table of n, a(n) for n=1..27.

Formula

row n+1 : f(0,r), f(1,r),...f(n,r), where f(k,r)=(k-th elementary symmetric function), r=(row n).

Example

First five rows:
2
1....2
1....3......2
1....6......11......6
1....24....191....564....396
The factorization property is illustrated by
x^2 + 3x + 2 -> (x+1)(x+3)(x+2) = x^3 + 6x^2 + 11x + 6.

Mathematica

s =.; s[1] = {2};
Prepend[Table[s[z] = Table[SymmetricPolynomial
 [k, s[z - 1]], {k, 0, z - 1}], {z, 2, 7}], s[1]]
% // TableForm (* A203301 triangle *)
%% // Flatten  (* A203301 sequence *)
(* Peter J. C. Moses, Dec 30 2011 *)

Crossrefs

Cf. A203300.

Sequence in context: A205696 A029635 A372704 * A309853 A107456 A334864

Adjacent sequences: A203298 A203299 A203300 * A203302 A203303 A203304

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 31 2011

Status

approved