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