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

0,5

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.

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 *)

Prog

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

Crossrefs

Cf. A025591, A086781, A160089.

Sequence in context: A112220 A185278 A241065 * A160089 A259358 A290086

Adjacent sequences: A086373 A086374 A086375 * A086377 A086378 A086379

Keyword

nonn,easy

Author

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

Extensions

More terms from Sascha Kurz, Sep 22 2003

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

Status

approved