%I #3 Mar 30 2012 18:36:41
%S 1,1,1,1,0,1,1,1,0,1,1,-2,3,0,1,1,1,-2,4,0,1,1,-8,12,-4,5,0,1,1,23,
%T -51,25,-5,6,0,1,1,-164,361,-192,50,-6,7,0,1,1,1255,-2856,1630,-484,
%U 87,-7,8,0,1,1,-12108,27795,-16292,5065,-1026,140,-8,9,0,1,1,136061,-315068,188665,-60125,12604,-1925,212,-9,10,0,1
%N Triangle, read by rows, where T(n,k) = (k/n)*Sum_{d|n} A096800(d,k).
%C Triangle A096800 lists row polynomials P_n(y), that satisfy the g.f.: A096651(x,y) = Product_{n>=1} 1/(1-x^n)^[P_n(y)/n], with P_n(0)=0 for n>=1; the row sums of A096651^n form the n-dimensional partitions.
%e Rows begin:
%e [1],
%e [1,1],
%e [1,0,1],
%e [1,1,0,1],
%e [1,-2,3,0,1],
%e [1,1,-2,4,0,1],
%e [1,-8,12,-4,5,0,1],
%e [1,23,-51,25,-5,6,0,1],
%e [1,-164,361,-192,50,-6,7,0,1],
%e [1,1255,-2856,1630,-484,87,-7,8,0,1],
%e [1,-12108,27795,-16292,5065,-1026,140,-8,9,0,1],
%e [1,136061,-315068,188665,-60125,12604,-1925,212,-9,10,0,1],
%e [1,-1756686,4093515,-2490800,809665,-173358,27146,-3312,306,-10,11,0,1],...
%Y Cf. A096651, A096800.
%K sign,tabl
%O 1,12
%A _Paul D. Hanna_, Jul 13 2004