login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320321 Number of weakly unimodal compositions of n in which the greatest part occurs exactly ten times. 2

%I #6 Oct 24 2018 16:29:12

%S 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 18,22,29,36,47,58,74,90,113,136,168,202,247,296,361,432,524,628,759,

%U 908,1095,1308,1572,1876,2247,2676,3198,3800,4528,5372,6384,7558

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

%H Alois P. Heinz, <a href="/A320321/b320321.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^(10*n) / Product_{j=1..n-1} (1-x^j)^2.

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

%p `if`(10*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=10 of A247255.

%K nonn

%O 0,22

%A _Alois P. Heinz_, Oct 10 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 26 04:38 EDT 2024. Contains 375454 sequences. (Running on oeis4.)