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A086376 Maximal coefficient of the polynomial (1-x)*(1-x^2)*...*(1-x^n).

%I A086376 #27 Jan 31 2024 10:24:34
%S A086376 1,1,1,1,2,1,2,2,2,2,3,2,4,3,3,4,6,5,6,7,8,8,10,11,16,16,18,21,28,29,
%T A086376 34,41,50,56,66,80,100,114,131,158,196,225,263,320,388,455,532,644,
%U A086376 786,921,1083,1321,1600,1891,2218,2711,3280,3895,4588,5591,6780,8051,9519,11624
%N A086376 Maximal coefficient of the polynomial (1-x)*(1-x^2)*...*(1-x^n).
%H A086376 Alois P. Heinz, <a href="/A086376/b086376.txt">Table of n, a(n) for n = 0..1000</a>
%H A086376 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Signum equations and extremal coefficients</a>.
%H A086376 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 A086376 J. W. Meijer and M. Nepveu, <a href="http://www.ucbcba.edu.bo/Publicaciones/revistas/actanova/documentos/v4n1/v4.n1.Meijer.pdf">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]
%H A086376 E. M. Wright, <a href="http://dx.doi.org/10.1093/qmath/15.1.283">A closer estimate for a restricted partition function</a>, Q. J. Math. 15 (1964) 283-287.
%p A086376 A086376 := proc(n)
%p A086376         g := expand(mul( 1-x^k,k=1..n) );
%p A086376         convert(PolynomialTools[CoefficientVector](g, x), list):
%p A086376         max(%);
%p A086376 end proc:
%p A086376 seq(A086376(n),n=0..60) ; # _R. J. Mathar_, Jun 01 2011
%t A086376 b[0] = 1; b[n_] := b[n] = b[n-1]*(1-x^n) // Expand;
%t A086376 a[n_] := CoefficientList[b[n], x] // Max;
%t A086376 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Apr 13 2017 *)
%o A086376 (PARI) a(n)=vecmax(Vec(prod(k=1,n,1-x^k)));
%o A086376 vector(100,n,a(n-1)) \\ _Joerg Arndt_, Jan 31 2024
%Y A086376 Cf. A025591, A086781, A160089.
%K A086376 nonn,easy
%O A086376 0,5
%A A086376 Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 07 2003
%E A086376 More terms from _Sascha Kurz_, Sep 22 2003
%E A086376 a(0)=1 prepended by _Alois P. Heinz_, Apr 12 2017