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A107050 Denominators of coefficients that satisfy: 3^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107049(k)/a(k).

%I A107050 #4 Mar 30 2012 18:36:46
%S A107050 1,1,1,27,864,2700000,291600000,240145138800000,1967268977049600000,
%T A107050 1045487392432216473600000,13068592405402705920000000000,
%U A107050 3728621931719673008255139717120000000000
%N A107050 Denominators of coefficients that satisfy: 3^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107049(k)/a(k).
%F A107050 A107049(n)/a(n) = Sum_{k=0..n} T(n, k)*3^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).
%e A107050 3^0 = 1;
%e A107050 3^1 = 1 + (2)*1;
%e A107050 3^2 = 1 + (2)*2 + (1)*2^2;
%e A107050 3^3 = 1 + (2)*3 + (1)*3^2 + (11/27)*3^3;
%e A107050 3^4 = 1 + (2)*4 + (1)*4^2 + (11/27)*4^3 + (101/864)*4^4.
%e A107050 Initial coefficients are:
%e A107050 A107049/A107050 = {1, 2, 1, 11/27, 101/864, 71723/2700000,
%e A107050 1462111/291600000, 194269981673/240145138800000,
%e A107050 224103520039487/1967268977049600000, ...}.
%o A107050 (PARI) {a(n)=denominator(sum(k=0,n,3^k*(matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1]))}
%Y A107050 Cf. A107049, A107045/A107046, A107047/A107048 (y=2), A107051/A107052 (y=4), A107053/A107054 (y=5).
%K A107050 nonn,frac
%O A107050 0,4
%A A107050 _Paul D. Hanna_, May 10 2005