A086394 (-1) times minimal coefficient of the polynomial (1-x)*(1-x^2)*...*(1-x^n).

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 8, 10, 11, 12, 16, 19, 21, 23, 29, 34, 41, 46, 56, 68, 80, 92, 114, 135, 158, 182, 225, 269, 320, 369, 455, 544, 644, 753, 921, 1111, 1321, 1543, 1891, 2274, 2711, 3183, 3895, 4694, 5591, 6592, 8051, 9729, 11624

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 08 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• 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]
• J. W. Meijer and M. Nepveu, Euler's ship on the Pentagonal Sea, Acta Nova, Volume 4, No.1, December 2008. pp. 176-187. [From _Johannes W. Meijer_, Jun 21 2010]

Crossrefs

Cf. A086376.

Cf. A025591.

Programs

Maple

p:= proc(n) option remember; expand(
      `if`(n=0, 1, (x^n-1)*p(n-1)))
    end:
a:= n-> -min(coeffs(p(n))):
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 12 2017

Mathematica

p[n_] := p[n] = Expand[If[n == 0, 1, (x^n - 1)*p[n - 1]]];
a[n_] := -Min[CoefficientList[p[n], x]];
Table[a[n], {n, 1, 80}]; (* Jean-François Alcover, Dec 28 2021, after Alois P. Heinz *)

PARI

a(n)=-vecmin(vector(n*(n+1)/2,i,polcoeff(prod(k=1,n,1-x^k),i))) \\ Benoit Cloitre, Sep 12 2003

Extensions

More terms from Benoit Cloitre, Sep 12 2003

Further terms from Sascha Kurz, Sep 22 2003