|
EXAMPLE
|
E.g.f.: A(x) = x + 3*x^2/2! + 14*x^3/3! + 80*x^4/4! + 539*x^5/5! + 4179*x^6/6! + 36630*x^7/7! + 358056*x^8/8! + 3860922*x^9/9! + 45519870*x^10/10! + ...
The coefficients in Product_{k=1..n} (1+k*x+x^2), n>=0, form the triangle:
[1];
[(1), 1, 1];
[1,(3), 4, 3, 1];
[1, 6, (14), 18, 14, 6, 1];
[1, 10, 39, (80), 100, 80, 39, 10, 1];
[1, 15, 90, 285, (539), 660, 539, 285, 90, 15, 1];
[1, 21, 181, 840, 2339, (4179), 5038, 4179, 2339, 840, 181, 21, 1];
[1, 28, 329, 2128, 8400, 21392, (36630), 43624, 36630, 21392, 8400, 2128, 329, 28, 1]; ...
the coefficients in parenthesis form the initial terms of this sequence.
|