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A107045 Numerators 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) = a(n,k)/A107046(n,k).

%I A107045 #4 Mar 30 2012 18:36:46
%S A107045 1,-1,1,1,-1,1,-1,1,-1,1,-11,1,1,-1,1,-677,-61,7,1,-1,1,15311,-259,-1,
%T A107045 7,1,-1,1,1170049273,-971891,-54407,407,23,1,-1,1,541293087149,
%U A107045 426148171,-15993079,-58573,829,17,1,-1,1,-15074636799365429,31108643619709,-23328513449,-138374321,-53429,1501,47,1
%N A107045 Numerators 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) = a(n,k)/A107046(n,k).
%F A107045 Numerators of the matrix inverse of triangle A079901(n, k) = n^k.
%e A107045 These are the numerators of the triangle that begins:
%e A107045 1;
%e A107045 -1,1;
%e A107045 1/4,-1/2,1/4;
%e A107045 -1/108,1/18,-1/12,1/27;
%e A107045 -11/6912,1/576,1/192,-1/108,1/256;
%e A107045 -677/21600000,-61/360000,7/24000,1/2700,-1/1280,1/3125; ...
%e A107045 which equals the matrix inverse of triangle A079901(n,k)=n^k:
%e A107045 1;
%e A107045 1,1;
%e A107045 1,2,4;
%e A107045 1,3,9,27;
%e A107045 1,4,16,64,256;
%e A107045 1,5,25,125,625,3125; ...
%o A107045 (PARI) a(n,k)=numerator((matrix(n+1,n+1,r,c,if(r>=c,(r-1)^(c-1)))^-1)[n+1,k+1])
%Y A107045 Cf. A079901, A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).
%K A107045 sign,tabl,frac
%O A107045 0,11
%A A107045 _Paul D. Hanna_, May 10 2005