A320317 - OEIS

%I #7 Oct 24 2018 16:27:34

%S 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,

%T 160,209,264,340,430,549,690,877,1098,1385,1730,2169,2698,3369,4174,

%U 5185,6406,7923,9752,12018,14744,18099,22140,27082,33026,40274,48970

%N Number of weakly unimodal compositions of n in which the greatest part occurs exactly six times.

%H Alois P. Heinz, <a href="/A320317/b320317.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodality#Unimodal_function">Unimodality, Unimodal function</a>

%F G.f.: Sum_{n>=0} x^(6*n) / Product_{j=1..n-1} (1-x^j)^2.

%F a(n) ~ Pi^5 * 5! * exp(2*Pi*sqrt(n/3)) / (2^8 * 3^(13/4) * n^(15/4)). - _Vaclav Kotesovec_, Oct 24 2018

%p b:= proc(n, i) option remember; `if`(i>n, 0,

%p       `if`(6*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))

%p     end:

%p a:= n-> `if`(n=0, 1, b(n, 1)):

%p seq(a(n), n=0..70);

%Y Column k=6 of A247255.

%K nonn

%O 0,14

%A _Alois P. Heinz_, Oct 10 2018