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A107054 Denominators of coefficients that satisfy: 5^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107053(k)/a(k).

%I A107054 #4 Mar 30 2012 18:36:46
%S A107054 1,1,1,27,216,675000,72900000,60036284700000,491817244262400000,
%T A107054 261371848108054118400000,3267148101350676480000000000,
%U A107054 932155482929918252063784929280000000000
%N A107054 Denominators of coefficients that satisfy: 5^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107053(k)/a(k).
%F A107054 A107053(n)/a(n) = Sum_{k=0..n} T(n, k)*5^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).
%e A107054 5^0 = 1;
%e A107054 5^1 = 1 + (4)*1;
%e A107054 5^2 = 1 + (4)*2 + (4)*2^2;
%e A107054 5^3 = 1 + (4)*3 + (4)*3^2 + (76/27)*3^3;
%e A107054 5^4 = 1 + (4)*4 + (4)*4^2 + (76/27)*4^3 + (307/216)*4^4.
%e A107054 Initial coefficients are:
%e A107054 A107053/A107054 = {1, 4, 4, 76/27, 307/216, 380989/675000,
%e A107054 13464073/72900000, 3084163593839/60036284700000,
%e A107054 6109976845914041/491817244262400000, ...}
%o A107054 (PARI) {a(n)=denominator(sum(k=0,n,5^k*(matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1]))}
%Y A107054 Cf. A107051, A107045/A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4).
%K A107054 nonn,frac
%O A107054 0,4
%A A107054 _Paul D. Hanna_, May 10 2005