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A203301 Self-generating triangle based on symmetric functions. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A128118 A205696 A029635 * A107456 A165112 A256106

Adjacent sequences:  A203298 A203299 A203300 * A203302 A203303 A203304

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 31 2011

STATUS

approved

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Last modified August 17 06:13 EDT 2017. Contains 290635 sequences.