login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160983 Number of partitions of n where every part appears at least 13 times 1

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,

%T 1,2,1,2,3,3,3,5,4,5,6,6,6,8,7,8,9,11,10,12,12,14,14,15,15,18,17,18,

%U 19,21,23,23,24,26,27,29,29,31,32,33,35,36,37,42,41,46,46,50,51,58,58,63,63,71,71,81,83,89,92,101,104

%N Number of partitions of n where every part appears at least 13 times

%H R. H. Hardin, <a href="/A160983/b160983.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-13*x)) dx = -1.268360284879056481996044472640421046229516947156436515845... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(13*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,26

%A _R. H. Hardin_ Jun 01 2009

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)