cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A326626 Number of partitions of n into 10 squarefree parts.

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%I A326626 #23 Apr 15 2021 08:18:58
%S A326626 0,0,0,0,0,0,0,0,0,0,1,1,2,2,4,5,8,9,13,16,23,26,35,41,54,62,79,90,
%T A326626 115,130,161,182,224,251,303,341,408,456,539,601,709,786,915,1014,
%U A326626 1179,1299,1496,1649,1892,2078,2368,2597,2953,3230,3645,3986,4492,4895
%N A326626 Number of partitions of n into 10 squarefree parts.
%H A326626 David A. Corneth, <a href="/A326626/b326626.txt">Table of n, a(n) for n = 0..9999</a>
%H A326626 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326626 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^2 * mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q-r)^2, where mu is the Möbius function (A008683).
%F A326626 a(n) = A326627(n)/n for n > 0.
%t A326626 Table[Count[IntegerPartitions[n,{10}],_?(AllTrue[#,SquareFreeQ]&)],{n,0,60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 25 2019 *)
%Y A326626 Cf. A008683, A326627, A326628, A326629, A326630, A326631, A326632, A326633, A326634, A326635, A326636, A326637.
%K A326626 nonn
%O A326626 0,13
%A A326626 _Wesley Ivan Hurt_, Jul 14 2019