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

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, 34, 41, 50, 56, 66, 80, 100, 114, 131, 158, 196, 225, 263, 320, 388, 455, 532, 644, 786, 921, 1083, 1321, 1600, 1891, 2218, 2711, 3280, 3895, 4588, 5591, 6780, 8051, 9519, 11624

Offset: 0

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 07 2003

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..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]
• E. M. Wright, A closer estimate for a restricted partition function, Q. J. Math. 15 (1964) 283-287.

Crossrefs

Cf. A025591, A086781, A160089.

Programs

Maple

A086376 := proc(n)
        g := expand(mul( 1-x^k,k=1..n) );
        convert(PolynomialTools[CoefficientVector](g, x), list):
        max(%);
end proc:
seq(A086376(n),n=0..60) ; # R. J. Mathar, Jun 01 2011

Mathematica

b[0] = 1; b[n_] := b[n] = b[n-1]*(1-x^n) // Expand;
a[n_] := CoefficientList[b[n], x] // Max;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 13 2017 *)

PARI

a(n)=vecmax(Vec(prod(k=1,n,1-x^k)));
vector(100,n,a(n-1)) \\ Joerg Arndt, Jan 31 2024

Extensions

More terms from Sascha Kurz, Sep 22 2003

a(0)=1 prepended by Alois P. Heinz, Apr 12 2017