A320317 Number of weakly unimodal compositions of n in which the greatest part occurs exactly six times.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 14, 18, 25, 32, 44, 56, 75, 96, 126, 160, 209, 264, 340, 430, 549, 690, 877, 1098, 1385, 1730, 2169, 2698, 3369, 4174, 5185, 6406, 7923, 9752, 12018, 14744, 18099, 22140, 27082, 33026, 40274, 48970

Offset

0,14

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Wikipedia, Unimodality, Unimodal function

Formula

G.f.: Sum_{n>=0} x^(6*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^5 * 5! * exp(2*Pi*sqrt(n/3)) / (2^8 * 3^(13/4) * n^(15/4)). - Vaclav Kotesovec, Oct 24 2018

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(6*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
    end:
a:= n-> `if`(n=0, 1, b(n, 1)):
seq(a(n), n=0..70);

Crossrefs

Column k=6 of A247255.

Sequence in context: A234949 A269303 A276642 * A017846 A179053 A218949

Adjacent sequences: A320314 A320315 A320316 * A320318 A320319 A320320

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2018

Status

approved