0,8

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,...].

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

Sequence in context: A060780 A106333 A104748 this_sequence A021863 A086241 A132870

Adjacent sequences: A117332 A117333 A117334 this_sequence A117336 A117337 A117338

sign,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 09 2006