A320321 Number of weakly unimodal compositions of n in which the greatest part occurs exactly ten times.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 18, 22, 29, 36, 47, 58, 74, 90, 113, 136, 168, 202, 247, 296, 361, 432, 524, 628, 759, 908, 1095, 1308, 1572, 1876, 2247, 2676, 3198, 3800, 4528, 5372, 6384, 7558

Offset

0,22

Links

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

Wikipedia, Unimodality, Unimodal function

Formula

G.f.: Sum_{n>=0} x^(10*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^9 * 9! * exp(2*Pi*sqrt(n/3)) / (2^12 * 3^(21/4) * n^(23/4)). - Vaclav Kotesovec, Oct 24 2018

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(10*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=10 of A247255.

Sequence in context: A180648 A322605 A175740 * A215009 A281943 A120003

Adjacent sequences: A320318 A320319 A320320 * A320322 A320323 A320324

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2018

Status

approved