login
A320317
Number of weakly unimodal compositions of n in which the greatest part occurs exactly six times.
2
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 14, 18, 25, 32, 44, 56, 75, 96, 126, 160, 209, 264, 340, 430, 549, 690, 877, 1098, 1385, 1730, 2169, 2698, 3369, 4174, 5185, 6406, 7923, 9752, 12018, 14744, 18099, 22140, 27082, 33026, 40274, 48970
OFFSET
0,14
FORMULA
G.f.: Sum_{n>=0} x^(6*n) / Product_{j=1..n-1} (1-x^j)^2.
a(n) ~ Pi^5 * 5! * exp(2*Pi*sqrt(n/3)) / (2^8 * 3^(13/4) * n^(15/4)). - Vaclav Kotesovec, Oct 24 2018
MAPLE
b:= proc(n, i) option remember; `if`(i>n, 0,
`if`(6*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=6 of A247255.
Sequence in context: A234949 A269303 A276642 * A017846 A179053 A218949
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2018
STATUS
approved