A320318 Number of weakly unimodal compositions of n in which the greatest part occurs exactly seven times.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 19, 26, 33, 44, 56, 73, 92, 119, 149, 190, 238, 301, 375, 472, 586, 733, 908, 1129, 1394, 1727, 2124, 2619, 3213, 3946, 4824, 5904, 7196, 8776, 10667, 12965, 15714, 19045, 23019, 27816

Offset: 0

Author

Alois P. Heinz, Oct 10 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Wikipedia, Unimodality, Unimodal function

Crossrefs

Column k=7 of A247255.

Programs

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(7*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);

Formula

G.f.: Sum_{n>=0} x^(7*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^6 * 6! * exp(2*Pi*sqrt(n/3)) / (2^9 * 3^(15/4) * n^(17/4)). - Vaclav Kotesovec, Oct 24 2018