A320320 Number of weakly unimodal compositions of n in which the greatest part occurs exactly nine times.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 21, 28, 35, 46, 57, 73, 90, 113, 138, 172, 209, 258, 314, 385, 467, 572, 692, 843, 1020, 1238, 1493, 1808, 2175, 2624, 3152, 3790, 4540, 5447, 6509, 7786, 9287, 11080

Offset

0,20

Links

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

Wikipedia, Unimodality, Unimodal function

Formula

G.f.: Sum_{n>=0} x^(9*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^8 * 8! * exp(2*Pi*sqrt(n/3)) / (2^11 * 3^(19/4) * n^(21/4)). - Vaclav Kotesovec, Oct 24 2018

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(9*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=9 of A247255.

Sequence in context: A072227 A122427 A161597 * A263364 A296242 A331020

Adjacent sequences: A320317 A320318 A320319 * A320321 A320322 A320323

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2018

Status

approved