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%I #6 Jun 16 2016 23:27:25
%S 1,1,-1,1,-5,10,1,-12,59,-90,1,-22,203,-830,1320,1,-35,525,-3985,
%T 15374,-23640,1,-51,1135,-13665,93544,-342324,523440,1,-70,2170,
%U -37870,399889,-2542540,8997540,-13633200,1,-92,3794,-90440,1356929,-13076588,78896236,-271996080,409852800,1,-117,6198,-193410
%N This table shows the coefficients of sum formulas of n-th Fibonacci numbers (A000045). The k-th row (k>=1) contains T(i,k) for i=1 to k, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies F(n)= Sum_{i=1..k} T(i,k) * n^(k-i)/(k-1)!.
%e F(13)=233; substituting n=13 in the formula of the k-th row we obtain k=7 and the coefficients
%e T(i,7) will be the following: 1,-51,1135,-13665,93544,-342324,523440,
%e => F(13) = [13^6-51*13^5+1135*13^4-13665*13^3+93544*13^2-342324*13+523440]/6! = 233.
%Y Cf. A000045, A094638.
%K sign,tabl
%O 1,5
%A _André F. Labossière_, Nov 08 2004
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