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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
OFFSET
0,22
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2018
STATUS
approved