A091029 Signed array used for numerators of generating functions of the column sequences of array A090452.

1, 3, -2, 2, 6, -9, 3, 15, 0, -24, 18, -4, 5, 69, -75, -20, 60, -30, 5, 63, 217, -462, 225, 80, -120, 45, -6, 14, 462, 300, -1848, 1785, -525, -210, 210, -63, 7, 252, 2460, -1809, -4932, 8428, -5208, 1050, 448, -336, 84, -8, 42, 2556, 9747, -18775, -2655, 28296, -28182, 12726, -1890, -840, 504, -108, 9

Offset: 2

Author

Wolfdieter Lang, Dec 23 2003

Keywords

• sign
• tabf

Comments

The row polynomials P(m,x) := sum(a(m,k)*x^k,k=0..kmax(m)),m>=2, where kmax(m) := floor(3*m/2)-3=A032766(m-2)=[0,1,3,4,6,7,9,10,...], appear in the numerator of the g.f.s of the columns of A090452.

The sequence of the lengths of the rows is [1,2,4,5,7,8,10,11,13,14,...]=A001651(m-2)= floor((3*m-4)/2).

Examples

			[1]; [3,-2]; [2,6,-9,3]; [15,0,-24,18,-4]; ...
P(3,x)=3-2*x; P(5,x)=15-24*x^2+18*x^3-4*x^4.
		

Links

• W. Lang, First 9 rows.

Formula

a(m, k)=[x^k]P(m, x), with P(m, x) := ((1-x)^(2*m-3))*G(m, x)/x^ceiling(m/2) and the G(m, x) satisfy the hypergeometric differential difference eq. given in A090452.