Search: id:A101033
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%I A101033
%S A101033 1,1,2,3,2,15,51,65,27,6,148,945,2292,2776,1680,405,24,2290,19580,71965,
               145525,
%T A101033 175244,125950,50085,8505,120,41676,473072,2340400,6676835,12132890,14587261,
%U A101033 11619692,5290005,1752030,229635,720,943908,13132532,81977672,303352938,
               740797855
%V A101033 1,1,-2,-3,2,15,51,65,27,6,-148,-945,-2292,-2776,-1680,-405,24,2290,19580,
               71965,145525,
%W A101033 175244,125950,50085,8505,120,-41676,-473072,-2340400,-6676835,-12132890,
               -14587261,
%X A101033 -11619692,-5290005,-1752030,-229635,720,943908,13132532,81977672,303352938,
               740797855
%N A101033 Triangle read by rows giving the coefficients of general sum formulae 
               of n-th Lucas numbers (A000204). The k-th row (k>=1) contains T(i,
               k) for i=1 to 2*k-1, where T(i,k) satisfies L(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 A101033 R. D. Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
               lucasNbs.html">The Lucas Numbers in Pascal's Triangle</a>.
%H A101033 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/index.html">
               Sobalian Coefficients</a>.
%H A101033 A. F. Labossiere, <a href="http://members.lycos.co.uk/stereotomography/
               index.html">Miscellaneous</a>.
%e A101033 L(7)= (1/(7-1)!) * [ 7^(7-1) -{-1+2*(7-2)+3*C(7-2,2)}*7^(7-2) +{2+15*(7-3)+51*C(7-3,
               2)+65*C(7-3,3)
%e A101033 +27*C(7-3,4)}*7^(7-3) -{-6+148*(7-4)+945*C(7-4,2)+2292*C(7-4,3)}*7^(7-4) 
               +... ]
%e A101033 = (1/6!) * [ 7^6 -{-1+10+30}*7^5 +{2+60+306+260+27}*7^4 -{-6+444+2835+2292}*7^3 
               +{24+4580+19580}*7^2
%e A101033 -{-120+41676}*7 +{720} ] = (1/6!) * [ 7^6 -39*7^5 +655*7^4 -5565*7^3 
               +24184*7^2 -41556*7 +720 ]
%e A101033 = (1/720) * [ 117649 -655473 +1572655 -1908795 +1185016 -290892 +720 
               ] = 20880/720 = 29.
%Y A101033 Cf. A101032, A000204, A100492, A099731, A000045, A094216, A094638, A000108.
%Y A101033 Sequence in context: A160819 A164661 A104507 this_sequence A136454 A025522 
               A019228
%Y A101033 Adjacent sequences: A101030 A101031 A101032 this_sequence A101034 A101035 
               A101036
%K A101033 easy,sign,tabl
%O A101033 1,3
%A A101033 Andre F. Labossiere (boronali(AT)laposte.net), Nov 30 2004

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