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

1,7

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]

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 *)

Prog

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

Crossrefs

Cf. A086376.

Cf. A025591.

Sequence in context: A053278 A035466 A122521 * A029226 A093354 A374032

Adjacent sequences: A086391 A086392 A086393 * A086395 A086396 A086397

Keyword

nonn

Author

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

Extensions

More terms from Benoit Cloitre, Sep 12 2003

Further terms from Sascha Kurz, Sep 22 2003

Status

approved