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.
%I A309438 #10 Nov 07 2021 07:02:17
%S A309438 0,0,0,0,0,0,0,0,0,0,1,3,5,11,17,30,45,72,104,147,200,279,367,491,633,
%T A309438 825,1042,1330,1649,2063,2531,3116,3776,4597,5510,6627,7878,9381,
%U A309438 11058,13059,15275,17895,20802,24191,27942,32303,37099,42628,48719,55678
%N A309438 Number of prime parts in the partitions of n into 9 parts.
%H A309438 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309438 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (c(q) + c(p) + c(o) + c(m) + c(l) + c(k) + c(j) + c(i) + c(n-i-j-k-l-m-o-p-q)), where c = A010051.
%t A309438 Table[Count[Flatten[IntegerPartitions[n,{9}]],_?PrimeQ],{n,0,50}] (* _Harvey P. Dale_, Jun 12 2021 *)
%Y A309438 Cf. A010051, A259200.
%K A309438 nonn
%O A309438 0,12
%A A309438 _Wesley Ivan Hurt_, Aug 03 2019