A248810 Signed version of A164984.

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.

Links

Table of n, a(n) for n=0..65.

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

Cf. A164984, A193845, A077925, A045883.

Sequence in context: A021755 A272295 A164984 * A339904 A208610 A193823

Adjacent sequences: A248807 A248808 A248809 * A248811 A248812 A248813

Keyword

sign,tabl

Author

Derek Orr, Oct 14 2014

Status

approved