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A248810
Signed version of A164984.
1
1, -1, 1, 3, -3, 1, -5, 9, -5, 1, 11, -23, 19, -7, 1, -21, 57, -61, 33, -9, 1, 43, -135, 179, -127, 51, -11, 1, -85, 313, -493, 433, -229, 73, -13, 1, 171, -711, 1299, -1359, 891, -375, 99, -15, 1, -341, 1593, -3309, 4017, -3141, 1641, -573, 129, -17, 1, 683, -3527, 8211, -11343, 10299, -6423, 2787, -831, 163, -19, 1
OFFSET
0,4
COMMENTS
Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x+2)^0 + A_1*(x+2)^1 + A_2*(x+2)^2 + ... + A_n*(x+2)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
FORMULA
T(n,n-1) = -2*n+1 for n > 0.
T(n,n-2) = 2*(n-1)^2+1 for n > 1.
T(n,0) = A077925(n).
T(n,1) = (-1)^(n+1)*A045883(n).
Rows with odd n sum to 0.
Rows with even n sum to 1.
EXAMPLE
1;
-1, 1;
3, -3, 1;
-5, 9, -5, 1;
11, -23, 19, -7, 1;
-21, 57, -61, 33, -9, 1;
43, -135, 179, -127, 51, -11, 1;
-85, 313, -493, 433, -229, 73, -13, 1;
171, -711, 1299, -1359, 891, -375, 99, -15, 1;
-341, 1593, -3309, 4017, -3141, 1641, -573, 129, -17, 1;
683, -3527, 8211, -11343, 10299, -6423, 2787, -831, 163, -19, 1;
PROG
(PARI) for(n=0, 20, for(k=0, n, print1(1/k!*sum(i=0, n, ((-2)^(i-k)*prod(j=0, k-1, i-j))), ", ")))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Derek Orr, Oct 14 2014
STATUS
approved