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Triangle T read by rows: inverse of fibonomial triangle (A010048).
1

%I #7 Apr 19 2014 01:43:57

%S 1,-1,1,0,-1,1,1,0,-2,1,-1,3,0,-3,1,-6,-5,15,0,-5,1,35,-48,-40,60,0,

%T -8,1,181,455,-624,-260,260,0,-13,1,-6056,3801,9555,-6552,-1820,1092,

%U 0,-21,1,-3741,-205904,129234,162435,-74256,-12376,4641,0,-34,1

%N Triangle T read by rows: inverse of fibonomial triangle (A010048).

%C Conjecture: all rows except the first add to zero.

%H M. Dziemianczuk, <a href="http://arxiv.org/abs/0806.3626">On multi F-nomial coefficients and Inversion formula for F-nomial coefficients</a>, Preprint: arXiv:0806.3626, 23 Jun 2008

%F Conjecture: T(n+k, n) = A010048(n+k-1, k)*T(k, 1), n>1.

%F a(n,k) = A010048(n,k) * (Sum[s=1..n-k;(-1)^s * Sum[k1+k2+..+ks=n-k,ki>=1; C(n-k; k1,k2,...,ks)] ]) where C(n; k1,k2,...,ks) is a multi-F-nomial coefficient. - _Maciej Dziemianczuk_, Dec 21 2008

%e 1,

%e -1,1,

%e 0,-1,1,

%e 1,0,-2,1,

%e -1,3,0,-3,1,

%e -6,-5,15,0,-5,1,

%e 35,-48,-40,60,0,-8,1,

%e 181,455,-624,-260,260,0,-13,1,

%e -6056,3801,9555,-6552,-1820,1092,0,-21,1,

%Y First column is in A103995.

%K sign,tabl

%O 1,9

%A _Ralf Stephan_, Feb 24 2005