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A320320
Number of weakly unimodal compositions of n in which the greatest part occurs exactly nine times.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2018
STATUS
approved