A154930 - OEIS

%I #8 Sep 08 2013 19:59:24

%S 1,-2,1,5,-4,1,-15,14,-6,1,51,-50,27,-8,1,-188,187,-113,44,-10,1,731,

%T -730,468,-212,65,-12,1,-2950,2949,-1956,970,-355,90,-14,1,12235,

%U -12234,8291,-4356,1785,-550,119,-16,1,-51822,51821,-35643,19474,-8612,3021

%N Inverse of Fibonacci convolution array A154929.

%C Alternating sign version of A104259. Row sums are (-1)^n*A033321. First column is (-1)^n*A007317.

%F Riordan array ((1/(1+x))c(-x/(1+x)), (x/(1+x))c(x/(1+x))), c(x) the g.f. of A000108;

%F Riordan array ((sqrt(1+6x+5x^2)-x-1)/(2x(1+x)),(sqrt(1+6x+5x^2)-x-1)/ (2(1+x)));

%F Triangle T(n,k) = sum{j=0..n, (-1)^(n-k)*C(n,j)*C(2j-k,j-k)(k+1)/(j+1)}.

%F T(n,k) = T(n-1,k-1) -2*T(n-1,k) + Sum_{i, i>=0} T(n-1,k+1+i)*(-1)^i. - _Philippe Deléham_, Feb 23 2012

%e Triangle begins

%e 1,

%e -2, 1,

%e 5, -4, 1,

%e -15, 14, -6, 1,

%e 51, -50, 27, -8, 1,

%e -188, 187, -113, 44, -10, 1,

%e 731, -730, 468, -212, 65, -12, 1,

%e -2950, 2949, -1956, 970, -355, 90, -14, 1

%e Production array is

%e -2, 1,

%e 1, -2, 1,

%e -1, 1, -2, 1,

%e 1, -1, 1, -2, 1,

%e -1, 1, -1, 1, -2, 1,

%e 1, -1, 1, -1, 1, -2, 1,

%e -1, 1, -1, 1, -1, 1, -2, 1

%e or ((1-x-x^2)/(1+x),x) beheaded.

%Y Cf. A171567, A054336, A171488, A035324.

%K easy,sign,tabl

%O 0,2

%A _Paul Barry_, Jan 17 2009