OFFSET
0,3
COMMENTS
This is the transformation of the polynomial 1 + 2x + 3x^2 + 4x^3 + ... + n*x^(n-1)+(n+1)*x^n to the polynomial A_0*(x+1)^0 + A_1*(x+1)^1 + A_2*(x+1)^2 + ... + A_n*(x+1)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
FORMULA
EXAMPLE
1;
-1, 2;
2, -4, 3;
-2, 8, -9, 4;
3, -12, 21, -16, 5;
-3, 18, -39, 44, -25, 6;
4, -24, 66, -96, 80, -36, 7;
-4, 32, -102, 184, -200, 132, -49, 8;
5, -40, 150, -320, 430, -372, 203, -64, 9;
-5, 50, -210, 520, -830, 888, -637, 296, -81, 10
PROG
(PARI) T(n, k)=(k+1)*sum(i=0, n-k, (-1)^i*binomial(i+k+1, k+1))
for(n=0, 15, for(k=0, n, print1(T(n, k), ", ")))
CROSSREFS
KEYWORD
AUTHOR
Derek Orr, Oct 30 2014
STATUS
approved