A039910 Lower triangular matrix T = Pascal lower triangular matrix divided on the left by its entry-square.

1, 0, 1, 0, -2, 1, 0, 12, -6, 1, 0, -132, 66, -12, 1, 0, 2280, -1140, 210, -20, 1, 0, -56760, 28380, -5240, 510, -30, 1, 0, 1923600, -961800, 177660, -17360, 1050, -42, 1, 0, -85149960, 42574980, -7864920, 769090, -46760, 1932, -56, 1

Offset: 0

Author

Len Smiley

Keywords

• sign
• tabl

Comments

Reference is a solution to a problem of I. Gessel.

Examples

			1;
0,1;
0,-2,1;
0,12,-6,1;
0,-132,66,-12,1;
etc.
		

References

• "Inverse of a Combinatorial Matrix", Dave Callan, American Mathematical Monthly, Vol. 95 (1988), pp. 770-771.

Crossrefs

A007318, A008459.

Formula

T=Inverse matrix of {a_ij}:{binomial(i, j)*binomial(j, j-i)}=[ A008459 ]^(-1)*[ A007318 ]