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A320318
Number of weakly unimodal compositions of n in which the greatest part occurs exactly seven times.
2
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 19, 26, 33, 44, 56, 73, 92, 119, 149, 190, 238, 301, 375, 472, 586, 733, 908, 1129, 1394, 1727, 2124, 2619, 3213, 3946, 4824, 5904, 7196, 8776, 10667, 12965, 15714, 19045, 23019, 27816
OFFSET
0,16
FORMULA
G.f.: Sum_{n>=0} x^(7*n) / Product_{j=1..n-1} (1-x^j)^2.
a(n) ~ Pi^6 * 6! * exp(2*Pi*sqrt(n/3)) / (2^9 * 3^(15/4) * n^(17/4)). - Vaclav Kotesovec, Oct 24 2018
MAPLE
b:= proc(n, i) option remember; `if`(i>n, 0,
`if`(7*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=7 of A247255.
Sequence in context: A283364 A131617 A214321 * A005577 A263362 A336733
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2018
STATUS
approved