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A096797 Triangle of coefficients, read by row polynomials P_n(y), that satisfy the g.f.: A038497(x,y) = Product_{n>=1} 1/(1-x^n)^[P_n(y)/n], with P_n(0)=0 for n>=1 and P_0(0)=1.

%I A096797 #3 Mar 30 2012 18:36:41
%S A096797 1,3,1,8,0,1,16,-1,0,1,34,-15,0,0,1,54,-40,3,0,0,1,104,-119,21,0,0,0,
%T A096797 1,156,-260,88,-1,0,0,0,1,261,-576,305,-27,0,0,0,0,1,382,-1111,850,
%U A096797 -155,3,0,0,0,0,1,615,-2167,2167,-638,33,0,0,0,0,0,1,842,-3854,5056,-2164,240,-1,0,0,0,0,0,1
%N A096797 Triangle of coefficients, read by row polynomials P_n(y), that satisfy the g.f.: A038497(x,y) = Product_{n>=1} 1/(1-x^n)^[P_n(y)/n], with P_n(0)=0 for n>=1 and P_0(0)=1.
%C A096797 A038497 is the matrix square of partition triangle A008284. The first column forms the Moebius transform of {n*A000041(n), n>=1}. The inverse Moebius transform of each column forms the columns of triangle {n/k*A096798(n,k)}.
%e A096797 1/A038497(x,y) =
%e A096797 (1-x)^y*(1-x^2)^[(3y+y^2)/2]*(1-x^3)^[(8y+y^3)/3]*(1-x^4)^[(16y-y^2+y^4)/
%e A096797 4]*(1-x^5)^[(34y-15y^2+y^5)/5]*...
%e A096797 Rows begin:
%e A096797 [1],
%e A096797 [3,1],
%e A096797 [8,0,1],
%e A096797 [16,-1,0,1],
%e A096797 [34,-15,0,0,1],
%e A096797 [54,-40,3,0,0,1],
%e A096797 [104,-119,21,0,0,0,1],
%e A096797 [156,-260,88,-1,0,0,0,1],
%e A096797 [261,-576,305,-27,0,0,0,0,1],
%e A096797 [382,-1111,850,-155,3,0,0,0,0,1],
%e A096797 [615,-2167,2167,-638,33,0,0,0,0,0,1],
%e A096797 [842,-3854,5056,-2164,240,-1,0,0,0,0,0,1],
%e A096797 [1312,-6916,11089,-6409,1183,-39,0,0,0,0,0,0,1],
%e A096797 [1782,-11649,23037,-17241,4704,-343,3,0,0,0,0,0,0,1],...
%Y A096797 Cf. A038497, A008284, A096798.
%K A096797 sign,tabl
%O A096797 1,2
%A A096797 _Paul D. Hanna_, Jul 13 2004