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A107047 Numerators of coefficients that satisfy: 2^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107048(k).

%I A107047 #4 Mar 30 2012 18:36:46
%S A107047 1,1,1,7,77,32387,395159,31824093937,44855117331581,
%T A107047 1825389561156191099,1571879809058619206897,
%U A107047 28070265610073576492663157851903,2782861136717279135850604073374039
%N A107047 Numerators of coefficients that satisfy: 2^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107048(k).
%C A107047 Sum_{k>=0} a(k)/A107048(k) = 2.3276417590495914492697647475269004042620542650376396714...
%F A107047 a(n)/A107048(n) = Sum_{k=0..n} T(n, k)*2^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).
%e A107047 2^0 = 1;
%e A107047 2^1 = 1 + 1;
%e A107047 2^2 = 1 + 1*2 + (1/4)*2^2;
%e A107047 2^3 = 1 + 1*3 + (1/4)*3^2 + (7/108)*3^3;
%e A107047 2^4 = 1 + 1*4 + (1/4)*4^2 + (7/108)*4^3 + (77/6912)*4^4.
%e A107047 Initial fractional coefficients are:
%e A107047 A107047/A107048 = {1, 1, 1/4, 7/108, 77/6912, 32387/21600000,
%e A107047 395159/2332800000, 31824093937/1921161110400000,
%e A107047 44855117331581/31476303632793600000, ... }.
%o A107047 (PARI) {a(n)=numerator(sum(k=0,n,2^k*(matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1]))}
%Y A107047 Cf. A107045/A107046, A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).
%K A107047 nonn,frac
%O A107047 0,4
%A A107047 _Paul D. Hanna_, May 10 2005