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A320318 Number of weakly unimodal compositions of n in which the greatest part occurs exactly seven times.

%I A320318 #7 Oct 24 2018 16:28:00
%S A320318 1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,2,3,4,5,6,7,9,11,15,19,26,33,44,56,73,
%T A320318 92,119,149,190,238,301,375,472,586,733,908,1129,1394,1727,2124,2619,
%U A320318 3213,3946,4824,5904,7196,8776,10667,12965,15714,19045,23019,27816
%N A320318 Number of weakly unimodal compositions of n in which the greatest part occurs exactly seven times.
%H A320318 Alois P. Heinz, <a href="/A320318/b320318.txt">Table of n, a(n) for n = 0..10000</a>
%H A320318 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodality#Unimodal_function">Unimodality, Unimodal function</a>
%F A320318 G.f.: Sum_{n>=0} x^(7*n) / Product_{j=1..n-1} (1-x^j)^2.
%F A320318 a(n) ~ Pi^6 * 6! * exp(2*Pi*sqrt(n/3)) / (2^9 * 3^(15/4) * n^(17/4)). - _Vaclav Kotesovec_, Oct 24 2018
%p A320318 b:= proc(n, i) option remember; `if`(i>n, 0,
%p A320318       `if`(7*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
%p A320318     end:
%p A320318 a:= n-> `if`(n=0, 1, b(n, 1)):
%p A320318 seq(a(n), n=0..70);
%Y A320318 Column k=7 of A247255.
%K A320318 nonn
%O A320318 0,16
%A A320318 _Alois P. Heinz_, Oct 10 2018