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A096800 Triangle of coefficients, read by 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.

%I A096800 #3 Mar 30 2012 18:36:41
%S A096800 1,1,1,2,0,1,2,1,0,1,4,-5,5,0,1,2,2,-5,6,0,1,6,-28,28,-7,7,0,1,4,90,
%T A096800 -136,49,-8,8,0,1,6,-738,1082,-432,90,-9,9,0,1,4,6279,-9525,4075,-969,
%U A096800 145,-10,10,0,1,10,-66594,101915,-44803,11143,-1881,220,-11,11,0,1,4,816362,-1260268,565988,-144300,25207,-3300,318
%N A096800 Triangle of coefficients, read by 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.
%C A096800 Row sums form the positive integers. The first column forms the totients (A000010). The inverse Moebius transform of each column forms the columns of triangle {n/k*A096799(n,k)}. A generalized Euler transform of the row polynomials of this triangle generates A096651; the row sums of A096651^n form the n-dimensional partitions.
%e A096800 G.f.: 1/A096651(x,y) = (1-x)^y*(1-x^2)^[(y+y^2)/2]*(1-x^3)^[(2y+y^3)/3]*(1-x^4)^[(2y+y^2+y^4)/4]*(1-x^5)^[(4y-5y^2+5y^3+y^5)/5]*...
%e A096800 Rows begin:
%e A096800 [1],
%e A096800 [1,1],
%e A096800 [2,0,1],
%e A096800 [2,1,0,1],
%e A096800 [4,-5,5,0,1],
%e A096800 [2,2,-5,6,0,1],
%e A096800 [6,-28,28,-7,7,0,1],
%e A096800 [4,90,-136,49,-8,8,0,1],
%e A096800 [6,-738,1082,-432,90,-9,9,0,1],
%e A096800 [4,6279,-9525,4075,-969,145,-10,10,0,1],
%e A096800 [10,-66594,101915,-44803,11143,-1881,220,-11,11,0,1],
%e A096800 [4,816362,-1260268,565988,-144300,25207,-3300,318,-12,12,0,1],
%e A096800 [12,-11418459,17738565,-8095100,2105129,-375609,50414,-5382,442,-13,13,0,1],...
%Y A096800 Cf. A096651, A096799.
%K A096800 sign,tabl
%O A096800 0,4
%A A096800 _Paul D. Hanna_, Jul 13 2004