cp's OEIS Frontend

A320319 Number of weakly unimodal compositions of n in which the greatest part occurs exactly eight times.

%I A320319 #6 Oct 24 2018 16:28:28
%S A320319 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,
%T A320319 56,73,90,115,142,179,220,276,338,421,516,638,780,962,1172,1438,1750,
%U A320319 2138,2594,3159,3822,4638,5600,6771,8154,9834,11812,14203,17024
%N A320319 Number of weakly unimodal compositions of n in which the greatest part occurs exactly eight times.
%H A320319 Alois P. Heinz, <a href="/A320319/b320319.txt">Table of n, a(n) for n = 0..10000</a>
%H A320319 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodality#Unimodal_function">Unimodality, Unimodal function</a>
%F A320319 G.f.: Sum_{n>=0} x^(8*n) / Product_{j=1..n-1} (1-x^j)^2.
%F A320319 a(n) ~ Pi^7 * 7! * exp(2*Pi*sqrt(n/3)) / (2^10 * 3^(17/4) * n^(19/4)). - _Vaclav Kotesovec_, Oct 24 2018
%p A320319 b:= proc(n, i) option remember; `if`(i>n, 0,
%p A320319       `if`(8*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
%p A320319     end:
%p A320319 a:= n-> `if`(n=0, 1, b(n, 1)):
%p A320319 seq(a(n), n=0..70);
%Y A320319 Column k=8 of A247255.
%K A320319 nonn
%O A320319 0,18
%A A320319 _Alois P. Heinz_, Oct 10 2018