%I A100492
%S A100492 1,1,4,3,10,49,95,83,27,90,740,2415,4110,3890,1950,405,1320,14054,64116,
%T A100492 164059,258461,257604,159070,55755,8505,23640,318684,1881532,6452300,14294605,
%U A100492 21442540,22106669,15496012,7078575,1905120,229635,523440,8474100,61424596
%V A100492 1,-1,-4,-3,10,49,95,83,27,-90,-740,-2415,-4110,-3890,-1950,-405,1320,
               14054,64116,
%W A100492 164059,258461,257604,159070,55755,8505,-23640,-318684,-1881532,-6452300,
               -14294605,
%X A100492 -21442540,-22106669,-15496012,-7078575,-1905120,-229635,523440,8474100,
               61424596
%N A100492 Triangle read by rows giving the coefficients of general sum formulae 
               of n-th Fibonacci numbers (A000045). The k-th row (k>=1) contains 
               T(i,k) for i=1 to 2*k-1, where T(i,k) satisfies F(n) = Sum_{k=1..n} 
               Sum_{i=1..2*k-1} T(i,k) * C(n-k,i-1) * n^(n-k) / (n-1)!.
%H A100492 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A100492 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%e A100492 F(7) = (1/(7-1)!) * [ 7^(7-1) -{1+4*(7-2)+3*C(7-2,2)}*7^(7-2) +{10+49*(7-3)+95*C(7-3,
               2)+83*C(7-3,3) +27*C(7-3,4)}*7^(7-3) -{90+740*(7-4)+2415*C(7-4,2)+4110*C(7-4,
               3)}*7^(7-4) +... ]
%e A100492 = (1/6!) * [ 7^6 -{1+20+30}*7^5 +{10+196+570+332+27}*7^4 -{90+2220+7245+4110}*7^3 
               +{1320+28108 +64116}*7^2 -{23640+318684}*7 +{523440} ]
%e A100492 = (1/6!) * [ 7^6 -51*7^5 +1135*7^4 -13665*7^3 +93544*7^2 -342324*7 +523440 
               ]
%e A100492 = (1/720) * [ 117649 -857157 +2725135 -4687095 +4583656 -2396268 +523440 
               ] = 9360/720 = 13.
%Y A100492 Cf. A099731, A000045, A094216, A094638, A000108.
%Y A100492 Sequence in context: A081617 A103252 A065763 this_sequence A072183 A005013 
               A086564
%Y A100492 Adjacent sequences: A100489 A100490 A100491 this_sequence A100493 A100494 
               A100495
%K A100492 easy,sign,tabl
%O A100492 1,3
%A A100492 Andre F. Labossiere (boronali(AT)laposte.net), Nov 22 2004