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%I #4 Mar 30 2012 18:36:46
%S 1,3,9,5,127,124273,385829,70009765747,220026935042111,
%T 59574747365570286907,113453152114585319883313,
%U 4471148647570383262775217527741887
%N Numerators of coefficients that satisfy: 4^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107052(k).
%C Sum_{k>=0} a(k)/A107052(k) = 8.2025187671791748426202820386803825244610468145759213023...
%F a(n)/A107052(n) = Sum_{k=0..n} T(n, k)*4^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).
%e 4^0 = 1;
%e 4^1 = 1 + (3)*1;
%e 4^2 = 1 + (3)*2 + (9/4)*2^2;
%e 4^3 = 1 + (3)*3 + (9/4)*3^2 + (5/4)*3^3;
%e 4^4 = 1 + (3)*4 + (9/4)*4^2 + (5/4)*4^3 + (127/256)*4^4.
%e Initial coefficients are:
%e A107051/A107052 = {1, 3, 9/4, 5/4, 127/256, 124273/800000,
%e 385829/9600000, 70009765747/7906012800000,
%e 220026935042111/129532113715200000, ...}.
%o (PARI) {a(n)=numerator(sum(k=0,n,4^k*(matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1]))}
%Y Cf. A107052, A107045/A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107053/A107054 (y=5).
%K nonn,frac
%O 0,2
%A _Paul D. Hanna_, May 10 2005
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