OFFSET
0,2
COMMENTS
Consider the transformation 1 + 2x + 3x^2 + 4x^3 + ... + (n+1)*x^n = A_0*(x+3)^0 + A_1*(x+3)^1 + A_2*(x+3)^2 + ... + A_n*(x+3)^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
Triangle starts:
1;
-5, 2;
22, -16, 3;
-86, 92, -33, 4;
319, -448, 237, -56, 5;
-1139, 1982, -1383, 484, -85, 6;
3964, -8224, 7122, -3296, 860, -120, 7;
-13532, 32600, -33702, 19384, -6700, 1392, -161, 8;
45517, -124864, 150006, -103088, 44330, -12216, 2107, -208, 9;
-151313, 465626, -637314, 509272, -261850, 89844, -20573, 3032, -261, 10;
...
PROG
(PARI) T(n, k) = (k+1)*sum(i=0, n-k, (-3)^i*binomial(i+k+1, k+1))
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Derek Orr, Nov 15 2014
STATUS
approved