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A117335 Matrix inverse of triangle A117334. 4

%I

%S 1,1,1,1,-1,1,1,6,-4,1,1,-27,24,-8,1,1,164,-157,66,-13,1,1,-1133,1176,

%T -571,146,-19,1,1,8930,-9853,5335,-1621,281,-26,1,1,-78739,91498,

%U -53989,18635,-3909,491,-34,1,1,768276,-933451,591157,-225490,54430,-8382,799,-43,1

%N Matrix inverse of triangle A117334.

%e Triangle begins:

%e 1;

%e 1,1;

%e 1,-1,1;

%e 1,6,-4,1;

%e 1,-27,24,-8,1;

%e 1,164,-157,66,-13,1;

%e 1,-1133,1176,-571,146,-19,1;

%e 1,8930,-9853,5335,-1621,281,-26,1;

%e 1,-78739,91498,-53989,18635,-3909,491,-34,1;

%e 1,768276,-933451,591157,-225490,54430,-8382,799,-43,1; ...

%e Matrix inverse yields A117334:

%e 1;

%e -1,1;

%e -2,1,1;

%e -3,-2,4,1;

%e -4,-13,8,8,1;

%e -5,-44,-3,38,13,1;

%e -6,-123,-117,125,101,19,1;

%e -7,-314,-718,205,594,213,26,1; ...

%e in which column k+1 is the Binomial transform of column k

%e preceded by a zero (includes the k zeros above diagonal):

%e column 1 = BINOMIAL[0, 1,-1,-2,-3,-4,-5,...]

%e = [0,1,1,-2,-13,-44,-123,-314,-761,...];

%e column 2 = BINOMIAL[0, 0,1,1,-2,-13,-44,-123,-314,...]

%e = [0,0,1,4,8,-3,-117,-718,-3314,...].

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

%K sign,tabl

%O 0,8

%A _Paul D. Hanna_, Mar 09 2006

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)