cp's OEIS Frontend

A320321 Number of weakly unimodal compositions of n in which the greatest part occurs exactly ten times.

%I A320321 #6 Oct 24 2018 16:29:12
%S A320321 1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,12,14,
%T A320321 18,22,29,36,47,58,74,90,113,136,168,202,247,296,361,432,524,628,759,
%U A320321 908,1095,1308,1572,1876,2247,2676,3198,3800,4528,5372,6384,7558
%N A320321 Number of weakly unimodal compositions of n in which the greatest part occurs exactly ten times.
%H A320321 Alois P. Heinz, <a href="/A320321/b320321.txt">Table of n, a(n) for n = 0..10000</a>
%H A320321 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodality#Unimodal_function">Unimodality, Unimodal function</a>
%F A320321 G.f.: Sum_{n>=0} x^(10*n) / Product_{j=1..n-1} (1-x^j)^2.
%F A320321 a(n) ~ Pi^9 * 9! * exp(2*Pi*sqrt(n/3)) / (2^12 * 3^(21/4) * n^(23/4)). - _Vaclav Kotesovec_, Oct 24 2018
%p A320321 b:= proc(n, i) option remember; `if`(i>n, 0,
%p A320321       `if`(10*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
%p A320321     end:
%p A320321 a:= n-> `if`(n=0, 1, b(n, 1)):
%p A320321 seq(a(n), n=0..70);
%Y A320321 Column k=10 of A247255.
%K A320321 nonn
%O A320321 0,22
%A A320321 _Alois P. Heinz_, Oct 10 2018