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A320321 Number of weakly unimodal compositions of n in which the greatest part occurs exactly ten times. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 22 10:47 EDT 2021. Contains 343174 sequences. (Running on oeis4.)