cp's OEIS Frontend

A106180 Matrix inverse of number triangle A046854.

%I A106180 #14 Jan 22 2020 03:32:28
%S A106180 1,-1,1,0,-1,1,1,-1,-1,1,0,2,-2,-1,1,-2,2,3,-3,-1,1,0,-5,5,4,-4,-1,1,
%T A106180 5,-5,-9,9,5,-5,-1,1,0,14,-14,-14,14,6,-6,-1,1,-14,14,28,-28,-20,20,7,
%U A106180 -7,-1,1,0,-42,42,48,-48,-27,27
%N A106180 Matrix inverse of number triangle A046854.
%C A106180 First column is A105523; second column is A106181.
%C A106180 Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Sep 29 2006
%C A106180 A124448*A007318 as infinite lower triangular matrices. - _Philippe Deléham_, Oct 16 2007
%F A106180 Riordan array (1-y, y) where y=-(1-sqrt(1+4x^2))/(2x).
%F A106180 Sum_{k=0..n} abs(T(n,k)) = A063886(n). - _Philippe Deléham_, Oct 06 2006
%F A106180 T(0,0)=1; T(n,k)=0 if k < 0 or if k > n; T(n,0) = -T(n-1,0) - T(n-1,1); T(n,k) = T(n,k-1) - T(n-1,k+1) for k >= 1. - _Philippe Deléham_, Oct 27 2007
%F A106180 T(2n,0) = A000007(n); T(2n+2,2k+2) = -T(2n+2,2k+1) = (-1)^(n-k)*A039598(n,k); T(2n+1,2k+1) = -T(2n+1,2k) = (-1)^(n-k)*A039599(n,k). - _Philippe Deléham_, Oct 29 2007
%F A106180 Sum_{k>=0} T(m,k)*T(n,k)*(-1)^k = T(m+n,0) = A105523(m+n). - _Philippe Deléham_, Jan 24 2010
%e A106180 Triangle begins
%e A106180    1;
%e A106180   -1,  1;
%e A106180    0, -1,  1;
%e A106180    1, -1, -1,  1;
%e A106180    0,  2, -2, -1,  1;
%e A106180   -2,  2,  3, -3, -1,  1;
%e A106180    0, -5,  5,  4, -4, -1,  1;
%Y A106180 Cf. A000108.
%K A106180 easy,sign,tabl
%O A106180 0,12
%A A106180 _Paul Barry_, Apr 24 2005