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%I #3 Mar 31 2012 13:20:05
%S 1,2,0,-10,15,25,30,475,450,125,6000,8500,6250,5000,1250,96000,146250,
%T 189375,159375,65625,9375,180000,5355000,8881250,5578125,2515625,
%U 721875,78125,44100000,254700000,341775000
%N Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000204(n+1), n >= 0 (Lucas numbers).
%C The row polynomials pL2(n,x) := sum(a(n,m)*x^m,m=0..n) and pL1(n,x) := sum(A061188(n,m)*x^m,m=0..n) appear in the k-fold convolution of the Lucas numbers L(n+1)= A000204(n+1)= A000032(n+1), n >= 0, as follows: L(k; n) := A060922(n+k,k)= (pL1(k,n)*L(n+2)+pL2(k,n)*L(n+1)/(k!*5^k).
%e {1}; {2,0}; {-10,15,25}; {30,475,450,125}; ...; pL2(2,n)=5*(-2+3*n+5*n^2)= 5*(1+n)*(-2+5*n).
%e L(2; n) := A060922(n+2,2)= A060929(n) = (1+n)*((4+5*n)*L(n+2)+(-2+5*n)*L(n+1))/(2*5).
%Y A061188(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).
%K sign,tabl
%O 0,2
%A _Wolfdieter Lang_, Apr 20 2001
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