A156082 Maximum coefficient of the polynomial (-1)^(n+1)*Product_{k=1..n} (1 - x^k)^2.

1, 2, 3, 4, 6, 8, 12, 19, 24, 36, 52, 74, 103, 156, 223, 322, 470, 682, 992, 1448, 2120, 3072, 4494, 6538, 9584, 14001, 20400, 29928, 43774, 64032, 93968, 137520, 201766, 296236, 433746, 637812, 936334, 1373622, 2021344, 2968872, 4364300, 6422472

Offset: 1

Author

Steven Finch, Feb 03 2009

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..2405
• S. R. Finch, Signum equations and extremal coefficients.
• Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]

Crossrefs

Cf. A133871.

Programs

Maple

P:= -1:
for n from 1 to 100 do
  P:= expand(-P*(1-x^n)^2);
  A[n]:= max(coeffs(P,x));
od:
seq(A[i],i=1..100); # Robert Israel, Mar 02 2018

Mathematica

Table[ -Min[CoefficientList[Expand[(-1)^n*Product[(1 - x^k)^2, {k, 1, n}]],x]], {n, 1, 50}]

Extensions

Name edited by Robert Israel, Mar 02 2018