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Denominators of the triangle of coefficients T(n,k), read by rows, that satisfy: y^x = Sum_{n=0..x} R_n(y)*x^n for all nonnegative integers x, y, where R_n(y) = Sum_{k=0..n} T(n,k)*y^k and T(n,k) = A107045(n,k)/a(n,k).
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%I #4 Mar 30 2012 18:36:46

%S 1,1,1,4,2,4,108,18,12,27,6912,576,192,108,256,21600000,360000,24000,

%T 2700,1280,3125,2332800000,12960000,2592000,291600,46080,18750,46656,

%U 1921161110400000,1524731040000,43563744000,700131600,15805440,918750

%N Denominators of the triangle of coefficients T(n,k), read by rows, that satisfy: y^x = Sum_{n=0..x} R_n(y)*x^n for all nonnegative integers x, y, where R_n(y) = Sum_{k=0..n} T(n,k)*y^k and T(n,k) = A107045(n,k)/a(n,k).

%F Denominators of the matrix inverse of triangle A079901(n, k) = n^k.

%e These are the denominators of the triangle that begins:

%e 1;

%e -1,1;

%e 1/4,-1/2,1/4;

%e -1/108,1/18,-1/12,1/27;

%e -11/6912,1/576,1/192,-1/108,1/256;

%e -677/21600000,-61/360000,7/24000,1/2700,-1/1280,1/3125; ...

%e which equals the matrix inverse of triangle A079901(n,k)=n^k:

%e 1;

%e 1,1;

%e 1,2,4;

%e 1,3,9,27;

%e 1,4,16,64,256;

%e 1,5,25,125,625,3125; ...

%o (PARI) a(n,k)=denominator((matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1])

%Y Cf. A079901, A107045, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).

%K nonn,tabl,frac

%O 0,4

%A _Paul D. Hanna_, May 10 2005