A096799 Triangle, read by rows, where T(n,k) = (k/n)*Sum_{d|n} A096800(d,k).

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, -51, 25, -5, 6, 0, 1, 1, -164, 361, -192, 50, -6, 7, 0, 1, 1, 1255, -2856, 1630, -484, 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

Offset: 1

Author

Paul D. Hanna, Jul 13 2004

Keywords

• sign
• tabl

Comments

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.

Examples

			Rows begin:
[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,-51,25,-5,6,0,1],
[1,-164,361,-192,50,-6,7,0,1],
[1,1255,-2856,1630,-484,87,-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],
[1,-1756686,4093515,-2490800,809665,-173358,27146,-3312,306,-10,11,0,1],...
		

Crossrefs

Cf. A096651, A096800.