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!)
A246937 Number of partitions of n into 5 sorts of parts. 4

%I #16 Jan 02 2021 16:07:11

%S 1,5,30,155,805,4055,20455,102455,513230,2567230,12841130,64211380,

%T 321082905,1605444405,8027354055,40136925680,200685295955,

%U 1003427268205,5017139711105,25085702537730,125428529603755,627142668099880,3135713425289030,15678567227192655

%N Number of partitions of n into 5 sorts of parts.

%H Alois P. Heinz, <a href="/A246937/b246937.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{i>=1} 1/(1-5*x^i).

%F a(n) ~ c * 5^n, where c = Product_{k>=1} 1/(1-1/5^k) = 1.3152135557353452193080... . - _Vaclav Kotesovec_, Mar 19 2015

%F G.f.: Sum_{i>=0} 5^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Apr 12 2018

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1) +`if`(i>n, 0, 5*b(n-i, i))))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..25);

%t (O[x]^20 - 4/QPochhammer[5, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)

%t b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, 5 b[n-i, i]]]];

%t a[n_] := b[n, n];

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Jan 02 2021, after _Alois P. Heinz_ *)

%Y Column k=5 of A246935.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 08 2014

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 March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)