A320319 Number of weakly unimodal compositions of n in which the greatest part occurs exactly eight times.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 20, 27, 34, 45, 56, 73, 90, 115, 142, 179, 220, 276, 338, 421, 516, 638, 780, 962, 1172, 1438, 1750, 2138, 2594, 3159, 3822, 4638, 5600, 6771, 8154, 9834, 11812, 14203, 17024

Offset

0,18

Links

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

Wikipedia, Unimodality, Unimodal function

Formula

G.f.: Sum_{n>=0} x^(8*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^7 * 7! * exp(2*Pi*sqrt(n/3)) / (2^10 * 3^(17/4) * n^(19/4)). - Vaclav Kotesovec, Oct 24 2018

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(8*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=8 of A247255.

Sequence in context: A246080 A278619 A173925 * A263363 A061920 A062010

Adjacent sequences: A320316 A320317 A320318 * A320320 A320321 A320322

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2018

Status

approved