login
A320319
Number of weakly unimodal compositions of n in which the greatest part occurs exactly eight times.
2
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 20, 27, 34, 45, 56, 73, 90, 115, 142, 179, 220, 276, 338, 421, 516, 638, 780, 962, 1172, 1438, 1750, 2138, 2594, 3159, 3822, 4638, 5600, 6771, 8154, 9834, 11812, 14203, 17024
OFFSET
0,18
FORMULA
G.f.: Sum_{n>=0} x^(8*n) / Product_{j=1..n-1} (1-x^j)^2.
a(n) ~ Pi^7 * 7! * exp(2*Pi*sqrt(n/3)) / (2^10 * 3^(17/4) * n^(19/4)). - Vaclav Kotesovec, Oct 24 2018
MAPLE
b:= proc(n, i) option remember; `if`(i>n, 0,
`if`(8*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=8 of A247255.
Sequence in context: A246080 A278619 A173925 * A263363 A061920 A062010
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2018
STATUS
approved