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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). 11

%I #4 Mar 30 2012 18:36:46

%S 1,1,1,27,216,675000,72900000,60036284700000,491817244262400000,

%T 261371848108054118400000,3267148101350676480000000000,

%U 932155482929918252063784929280000000000

%N 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 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 5^0 = 1;

%e 5^1 = 1 + (4)*1;

%e 5^2 = 1 + (4)*2 + (4)*2^2;

%e 5^3 = 1 + (4)*3 + (4)*3^2 + (76/27)*3^3;

%e 5^4 = 1 + (4)*4 + (4)*4^2 + (76/27)*4^3 + (307/216)*4^4.

%e Initial coefficients are:

%e A107053/A107054 = {1, 4, 4, 76/27, 307/216, 380989/675000,

%e 13464073/72900000, 3084163593839/60036284700000,

%e 6109976845914041/491817244262400000, ...}

%o (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 Cf. A107051, A107045/A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4).

%K nonn,frac

%O 0,4

%A _Paul D. Hanna_, May 10 2005

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)