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A320317 Number of weakly unimodal compositions of n in which the greatest part occurs exactly six times.

%I A320317 #7 Oct 24 2018 16:27:34
%S A320317 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 A320317 160,209,264,340,430,549,690,877,1098,1385,1730,2169,2698,3369,4174,
%U A320317 5185,6406,7923,9752,12018,14744,18099,22140,27082,33026,40274,48970
%N A320317 Number of weakly unimodal compositions of n in which the greatest part occurs exactly six times.
%H A320317 Alois P. Heinz, <a href="/A320317/b320317.txt">Table of n, a(n) for n = 0..10000</a>
%H A320317 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodality#Unimodal_function">Unimodality, Unimodal function</a>
%F A320317 G.f.: Sum_{n>=0} x^(6*n) / Product_{j=1..n-1} (1-x^j)^2.
%F A320317 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 A320317 b:= proc(n, i) option remember; `if`(i>n, 0,
%p A320317       `if`(6*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
%p A320317     end:
%p A320317 a:= n-> `if`(n=0, 1, b(n, 1)):
%p A320317 seq(a(n), n=0..70);
%Y A320317 Column k=6 of A247255.
%K A320317 nonn
%O A320317 0,14
%A A320317 _Alois P. Heinz_, Oct 10 2018