cp's OEIS Frontend

A117335 Matrix inverse of triangle A117334.

%I A117335 #4 Mar 30 2012 18:36:56
%S A117335 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 A117335 -571,146,-19,1,1,8930,-9853,5335,-1621,281,-26,1,1,-78739,91498,
%U A117335 -53989,18635,-3909,491,-34,1,1,768276,-933451,591157,-225490,54430,-8382,799,-43,1
%N A117335 Matrix inverse of triangle A117334.
%e A117335 Triangle begins:
%e A117335 1;
%e A117335 1,1;
%e A117335 1,-1,1;
%e A117335 1,6,-4,1;
%e A117335 1,-27,24,-8,1;
%e A117335 1,164,-157,66,-13,1;
%e A117335 1,-1133,1176,-571,146,-19,1;
%e A117335 1,8930,-9853,5335,-1621,281,-26,1;
%e A117335 1,-78739,91498,-53989,18635,-3909,491,-34,1;
%e A117335 1,768276,-933451,591157,-225490,54430,-8382,799,-43,1; ...
%e A117335 Matrix inverse yields A117334:
%e A117335 1;
%e A117335 -1,1;
%e A117335 -2,1,1;
%e A117335 -3,-2,4,1;
%e A117335 -4,-13,8,8,1;
%e A117335 -5,-44,-3,38,13,1;
%e A117335 -6,-123,-117,125,101,19,1;
%e A117335 -7,-314,-718,205,594,213,26,1; ...
%e A117335 in which column k+1 is the Binomial transform of column k
%e A117335 preceded by a zero (includes the k zeros above diagonal):
%e A117335 column 1 = BINOMIAL[0, 1,-1,-2,-3,-4,-5,...]
%e A117335 = [0,1,1,-2,-13,-44,-123,-314,-761,...];
%e A117335 column 2 = BINOMIAL[0, 0,1,1,-2,-13,-44,-123,-314,...]
%e A117335 = [0,0,1,4,8,-3,-117,-718,-3314,...].
%Y A117335 Cf. A117334 (inverse), A117336 (column 1), A117337 (column 2), A117338 (row sums).
%K A117335 sign,tabl
%O A117335 0,8
%A A117335 _Paul D. Hanna_, Mar 09 2006