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.

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, -136, 49, -8, 8, 0, 1, 6, -738, 1082, -432, 90, -9, 9, 0, 1, 4, 6279, -9525, 4075, -969, 145, -10, 10, 0, 1, 10, -66594, 101915, -44803, 11143, -1881, 220, -11, 11, 0, 1, 4, 816362, -1260268, 565988, -144300, 25207, -3300, 318

Offset: 0

Author

Paul D. Hanna, Jul 13 2004

Keywords

• sign
• tabl

Comments

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.

Examples

			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]*...
Rows begin:
[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,-136,49,-8,8,0,1],
[6,-738,1082,-432,90,-9,9,0,1],
[4,6279,-9525,4075,-969,145,-10,10,0,1],
[10,-66594,101915,-44803,11143,-1881,220,-11,11,0,1],
[4,816362,-1260268,565988,-144300,25207,-3300,318,-12,12,0,1],
[12,-11418459,17738565,-8095100,2105129,-375609,50414,-5382,442,-13,13,0,1],...
		

Crossrefs

Cf. A096651, A096799.