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%I #10 Mar 30 2012 17:40:29
%S 1,-1,1,-1,-1,1,7,-2,-1,1,-13,12,-3,-1,1,-17,-22,18,-4,-1,1,199,-45,
%T -35,25,-5,-1,1,-605,465,-84,-53,33,-6,-1,1,-225,-1449,910,-133,-77,
%U 42,-7,-1,1,11703,-864,-3094,1594,-190,-108,52,-8,-1,1,-59317,33780,-1380,-6027,2583,-252,-147,63,-9,-1,1,83143,-179398,78567,-771,-10899,3948,-315,-195,75,-10,-1,1,991671,271073,-461978,159115,2882,-18546,5764,-374,-253,88,-11,-1,1
%N Triangle of polynomial coefficients of the polynomial factors defined in A074051.
%C The triangle T(n,k), 0<=k<n, shows the coefficients [x^k] of the polynomial p_n(x) which distributes sum_{i=1..m} i^n*(i+1)! = A074052(n) + A074051(n)*sum_{i=1..m} (i+1)! + p_n(m) *(m+2)!.
%F A074052(n) + 2*A074051(n) + 6*p_n(1) = 2. - R. J. Mathar, Oct 13 2011
%F (x+2)*p_n(x)-p_n(x-1) = x^n-A074051(n). - R. J. Mathar, Oct 13 2011
%F Conjectures on p_n(x)= sum_{k=0..n-1} T(n,k)*x^k:
%F T(n,n-1) = 1.
%F T(n,n-2) = -1.
%F T(n,n-3) = -(n-2).
%F T(n,n-4) = A055998(n-2).
%F T(n,n-5) = -(n-2)*(n^2-4*n+21)/6.
%F T(n,n-6) = (n-5)*(n-2)*(n^2-19*n-24)/24.
%e 1; 1
%e -1,1; -1+x
%e -1,-1,1; -1-x+x^2
%e 7,-2,-1,1; 7-2*x-x^2+x^3
%e -13,12,-3,-1,1; -13+12*x-3*x^2-x^3+x^4
%e -17,-22,18,-4,-1,1; -17-22*x+18*x^2-4*x^3-x^4+x^5
%K sign,tabl
%O 1,7
%A _R. J. Mathar_, Oct 11 2011
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