A120295 Absolute value of the largest coefficient of Product[(1-x^k)^k,{k,1,n}].

1, 2, 6, 30, 289, 5170, 155768, 7947236, 695357704, 105014923458, 27857098312474, 12416271212737642, 9302296598744837059, 12142590791028740988194, 26874517085010633423659616, 100413718348008543669377307304

Offset: 1

Author

Alexander Adamchuk, Jul 10 2006

Keywords

• nonn

Examples

			a(1)=1 because Product[(1-x^k)^k,{k,1,1}]=x-1.
a(2)=2 because Product[(1-x^k)^k,{k,1,2}]=(1-x)(1-x^2)^2=-x^5+x^4+2x^3-2x^2-x+1.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..92

Programs

Mathematica

Table[Max[Abs[CoefficientList[Product[(1-x^k)^k,{k,1,n}],x]]],{n,1,16}]
p=1; Table[p=Expand[p*(1-x^n)^n]; Max[Abs[CoefficientList[p,x]]],{n,1,20}] (* Vaclav Kotesovec, Feb 10 2015 *)

Formula

a(n) = Max[Abs[CoefficientList[Product[(1-x^k)^k,{k,1,n}],x]]].