A086394 - OEIS

%I #36 Dec 29 2021 09:50:38

%S 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,

%T 41,46,56,68,80,92,114,135,158,182,225,269,320,369,455,544,644,753,

%U 921,1111,1321,1543,1891,2274,2711,3183,3895,4694,5591,6592,8051,9729,11624

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

%H Alois P. Heinz, <a href="/A086394/b086394.txt">Table of n, a(n) for n = 1..1000</a>

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Signum equations and extremal coefficients</a>.

%H Steven R. Finch, <a href="/A000980/a000980.pdf">Signum equations and extremal coefficients</a>, February 7, 2009. [Cached copy, with permission of the author]

%H J. W. Meijer and M. Nepveu, <a href="http://www.scielo.org.bo/scielo.php?script=sci_abstract&amp;pid=S1683-07892008000100010">Euler's ship on the Pentagonal Sea</a>, Acta Nova, Volume 4, No.1, December 2008. pp. 176-187. [From _Johannes W. Meijer_, Jun 21 2010]

%p p:= proc(n) option remember; expand(

%p       `if`(n=0, 1, (x^n-1)*p(n-1)))

%p     end:

%p a:= n-> -min(coeffs(p(n))):

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Apr 12 2017

%t p[n_] := p[n] = Expand[If[n == 0, 1, (x^n - 1)*p[n - 1]]];

%t a[n_] := -Min[CoefficientList[p[n], x]];

%t Table[a[n], {n, 1, 80}]; (* _Jean-François Alcover_, Dec 28 2021, after _Alois P. Heinz_ *)

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

%Y Cf. A086376.

%Y Cf. A025591.

%K nonn

%O 1,7

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

%E More terms from _Benoit Cloitre_, Sep 12 2003

%E Further terms from _Sascha Kurz_, Sep 22 2003