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Triangle read by rows: lower triangular matrix which is inverse to the Fibonacci triangle (A139375) regarded as a lower triangular matrix.
1

%I #17 Mar 18 2020 14:51:40

%S 1,-1,1,0,-2,1,2,1,-3,1,-1,2,3,-4,1,0,-3,1,6,-5,1,0,1,-5,-2,10,-6,1,0,

%T 0,4,-6,-8,15,-7,1,0,0,-1,9,-4,-18,21,-8,1,0,0,0,-5,15,4,-33,28,-9,1,

%U 0,0,0,1,-14,19,22,-54,36,-10,1,0,0,0,0,6,-29,15,55,-82,45,-11,1,0,0,0,0,-1,20,-48,-7,109,-118,55,-12,1,0,0,0,0,0,-7,49,-63,-62,191,-163,66,-13,1

%N Triangle read by rows: lower triangular matrix which is inverse to the Fibonacci triangle (A139375) regarded as a lower triangular matrix.

%H Tian-Xiao He and Renzo Sprugnoli, <a href="https://doi.org/10.1016/j.disc.2008.11.021">Sequence characterization of Riordan arrays</a>, Discrete Math. 309 (2009), no. 12, 3962-3974.

%e Triangle begins

%e 1

%e -1 1

%e 0 -2 1

%e 2 1 -3 1

%e -1 2 3 -4 1

%e 0 -3 1 6 -5 1

%e 0 1 -5 -2 10 -6

%e ...

%p read("transforms3") ;

%p g := 1-x+2*x^3-x^4 ;

%p h := x*(1-x) ;

%p for n from 0 to 10 do

%p for k from 0 to n do

%p RIORDAN(g,h,n,k) ;

%p printf("%d,",%) ;

%p end do:

%p printf("\n") ;

%p end do: # _R. J. Mathar_, Dec 13 2011

%Y Cf. A139375.

%K sign,tabl

%O 0,5

%A _N. J. A. Sloane_, Nov 27 2011