|
EXAMPLE
|
A(x) = 1 + 7*x + 21*x^2 + 21*x^3 - 63*x^4 - 231*x^5 - 15*x^6 +-...
For n>=0, the first (n+1) coefficients of A(x)^(n+1) forms the
n-th row polynomial R_n(y) of triangle A097181:
A^1={1,_7,21,21,-63,-231,-15,1521,3073,...}
A^2={1,14,_91,336,609,-462,-5469,-9516,...}
A^3={1,21,210,_1288,5103,11655,2160,-85590,...}
A^4={1,28,378,3220,_18907,77280,199860,153000,...}
A^5={1,35,595,6475,49910,_283192,1175190,3282870,...}
A^6={1,42,861,11396,108402,778596,_4296034,17959968,...}
These row polynomials satisfy: R_n(1/2) = 8^n:
8^1 = 1 + 14/2;
8^2 = 1 + 21/2 + 210/2^2;
8^3 = 1 + 28/2 + 378/2^2 + 3220/2^3;
8^4 = 1 + 35/2 + 595/2^2 + 6475/2^3 + 49910/2^4.
|