A117335 Matrix inverse of triangle A117334.

1, 1, 1, 1, -1, 1, 1, 6, -4, 1, 1, -27, 24, -8, 1, 1, 164, -157, 66, -13, 1, 1, -1133, 1176, -571, 146, -19, 1, 1, 8930, -9853, 5335, -1621, 281, -26, 1, 1, -78739, 91498, -53989, 18635, -3909, 491, -34, 1, 1, 768276, -933451, 591157, -225490, 54430, -8382, 799, -43, 1

Offset: 0

Author

Paul D. Hanna, Mar 09 2006

Keywords

• sign
• tabl

Examples

			Triangle begins:
1;
1,1;
1,-1,1;
1,6,-4,1;
1,-27,24,-8,1;
1,164,-157,66,-13,1;
1,-1133,1176,-571,146,-19,1;
1,8930,-9853,5335,-1621,281,-26,1;
1,-78739,91498,-53989,18635,-3909,491,-34,1;
1,768276,-933451,591157,-225490,54430,-8382,799,-43,1; ...
Matrix inverse yields A117334:
1;
-1,1;
-2,1,1;
-3,-2,4,1;
-4,-13,8,8,1;
-5,-44,-3,38,13,1;
-6,-123,-117,125,101,19,1;
-7,-314,-718,205,594,213,26,1; ...
in which column k+1 is the Binomial transform of column k
preceded by a zero (includes the k zeros above diagonal):
column 1 = BINOMIAL[0, 1,-1,-2,-3,-4,-5,...]
= [0,1,1,-2,-13,-44,-123,-314,-761,...];
column 2 = BINOMIAL[0, 0,1,1,-2,-13,-44,-123,-314,...]
= [0,0,1,4,8,-3,-117,-718,-3314,...].
		

Crossrefs

Cf. A117334 (inverse), A117336 (column 1), A117337 (column 2), A117338 (row sums).