%I A099731
%S A099731 1,1,1,1,5,10,1,12,59,90,1,22,203,830,1320,1,35,525,3985,15374,23640,1,
               51,
%T A099731 1135,13665,93544,342324,523440,1,70,2170,37870,399889,2542540,8997540,
               13633200,
%U A099731 1,92,3794,90440,1356929,13076588,78896236,271996080,409852800,1,117,6198,
               193410
%V A099731 1,1,-1,1,-5,10,1,-12,59,-90,1,-22,203,-830,1320,1,-35,525,-3985,15374,
               -23640,1,-51,
%W A099731 1135,-13665,93544,-342324,523440,1,-70,2170,-37870,399889,-2542540,8997540,
               -13633200,
%X A099731 1,-92,3794,-90440,1356929,-13076588,78896236,-271996080,409852800,1,-117,
               6198,-193410
%N A099731 This table shows the coefficients of sum formulae 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)!.
%H A099731 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A099731 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%e A099731 F(13)=233; substituting n=13 in the formula of the k-th row we obtain 
               k=7 and the coefficients
%e A099731 T(i,7) will be the following: 1,-51,1135,-13665,93544,-342324,523440,
%e A099731 => F(13) = [13^6-51*13^5+1135*13^4-13665*13^3+93544*13^2-342324*13+523440]/
               6! = 233.
%Y A099731 Cf. A000045, A094638.
%Y A099731 Sequence in context: A101683 A098135 A112259 this_sequence A091306 A073048 
               A102258
%Y A099731 Adjacent sequences: A099728 A099729 A099730 this_sequence A099732 A099733 
               A099734
%K A099731 sign,tabl
%O A099731 1,5
%A A099731 Andre F. Labossiere (boronali(AT)laposte.net), Nov 08 2004