A124744 Expansion of (1+x*y)/(1-x^2*y^2+x^3*y^2).

1, 0, 1, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 1, -3, 1, 0, 0, 0, 0, 0, 0, 3, -3, 1, 0, 0, 0, 0, 0, 0, -1, 3, -4, 1, 0, 0, 0, 0, 0, 0, 0, -1, 6, -4, 1

Offset

0,20

Comments

Row sums are A124745. Diagonal sums are A124746. Inverse is A124747.

Links

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

Formula

Number triangle T(n,k)=C(floor(k/2),n-k)*(-1)^(n-k)

Column k has g.f. x^k*(1-x)^floor(k/2). - Paul Barry, Feb 01 2007

Example

Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, -1, 1,
0, 0, 0, -1, 1,
0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 1, -3, 1,
0, 0, 0, 0, 0, 0, 3, -3, 1,
0, 0, 0, 0, 0, 0, -1, 3, -4, 1,
0, 0, 0, 0, 0, 0, 0, -1, 6, -4, 1

Crossrefs

Sequence in context: A321854 A227839 A291748 * A124788 A284504 A281245

Adjacent sequences: A124741 A124742 A124743 * A124745 A124746 A124747

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 06 2006

Status

approved