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A113020 Number triangle whose row sums are the Fibonacci numbers.

%I A113020 #5 Oct 25 2012 07:02:09
%S A113020 0,0,1,0,2,-1,0,3,-3,2,0,4,-6,8,-3,0,5,-10,20,-15,5,0,6,-15,40,-45,30,
%T A113020 -8,0,7,-21,70,-105,105,-56,13,0,8,-28,112,-210,280,-224,104,-21,0,9,
%U A113020 -36,168,-378,630,-672,468,-189,34,0,10,-45,240,-630,1260,-1680,1560,-945,340,-55
%N A113020 Number triangle whose row sums are the Fibonacci numbers.
%C A113020 Row sums sequence is A000045, F(n).
%C A113020 Main diagonal is (-1)^(n+1)F(n).
%C A113020 Absolute row sums sequence is A001906, F(2n).
%C A113020 Diagonal sums are A113021.
%H A113020 Olivier Gérard, <a href="/A113020/b113020.txt">Table of n, a(n) for n = 0..230</a>
%F A113020 T(n, k)=sum{j=0..n, C(n, j)C(0, j-k)F(j-2k)}.
%e A113020 Rows begin
%e A113020 0;
%e A113020 0,1;
%e A113020 0,2,-1;
%e A113020 0,3,-3,2;
%e A113020 0,4,-6,8,-3;
%e A113020 0,5,-10,20,-15,5;
%e A113020 0,6,-15,40,-45,30,-8;
%e A113020 0,7,-21,70,-105,105,-56,13;
%t A113020 Flatten[Table[Table[Sum[Binomial[n,j]Binomial[0,j-k]Fibonacci[j-2k],{j,0,n}],{k,0,n}],{n,0,10}],1]
%Y A113020 Cf. A094435.
%K A113020 easy,sign,tabl
%O A113020 0,5
%A A113020 _Paul Barry_, Oct 11 2005
%E A113020 Values corrected and Mathematica program by _Olivier Gérard_, Oct 24 2012