A197184 Triangle of polynomial coefficients of the polynomial factors defined in A074051.

1, -1, 1, -1, -1, 1, 7, -2, -1, 1, -13, 12, -3, -1, 1, -17, -22, 18, -4, -1, 1, 199, -45, -35, 25, -5, -1, 1, -605, 465, -84, -53, 33, -6, -1, 1, -225, -1449, 910, -133, -77, 42, -7, -1, 1, 11703, -864, -3094, 1594, -190, -108, 52, -8, -1, 1, -59317, 33780, -1380, -6027, 2583, -252, -147, 63, -9, -1, 1, 83143, -179398, 78567, -771, -10899, 3948, -315, -195, 75, -10, -1, 1, 991671, 271073, -461978, 159115, 2882, -18546, 5764, -374, -253, 88, -11, -1, 1

Offset: 1

Author

R. J. Mathar, Oct 11 2011

Keywords

• sign
• tabl

Comments

The triangle T(n,k), 0<=kA074052(n) + A074051(n)*sum_{i=1..m} (i+1)! + p_n(m) *(m+2)!.

Examples

			1;   1
-1,1;  -1+x
-1,-1,1;  -1-x+x^2
7,-2,-1,1;  7-2*x-x^2+x^3
-13,12,-3,-1,1;  -13+12*x-3*x^2-x^3+x^4
-17,-22,18,-4,-1,1;   -17-22*x+18*x^2-4*x^3-x^4+x^5
		

Formula

A074052(n) + 2*A074051(n) + 6*p_n(1) = 2. - R. J. Mathar, Oct 13 2011

(x+2)*p_n(x)-p_n(x-1) = x^n-A074051(n). - R. J. Mathar, Oct 13 2011

Conjectures on p_n(x)= sum_{k=0..n-1} T(n,k)*x^k:

T(n,n-1) = 1.

T(n,n-2) = -1.

T(n,n-3) = -(n-2).

T(n,n-4) = A055998(n-2).

T(n,n-5) = -(n-2)*(n^2-4*n+21)/6.

T(n,n-6) = (n-5)*(n-2)*(n^2-19*n-24)/24.