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 A326461 #11 May 15 2025 19:06:11
%S A326461 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,5,5,8,10,12,14,19,21,27,34,35,
%T A326461 44,57,64,67,88,87,115,121,142,146,191,176,233,232,289,271,369,336,
%U A326461 455,414,537,500,687,588,816,722,974,843,1179,977,1392,1172
%N A326461 Sum of the third largest parts in the partitions of n into 8 primes.
%H A326461 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326461 a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p) * j, where c = A010051.
%F A326461 a(n) = A326455(n) - A326456(n) - A326457(n) - A326458(n) - A326459(n) - A326460(n) - A326462(n) - A326463(n).
%t A326461 Table[Total[Select[IntegerPartitions[n,{8}],AllTrue[#,PrimeQ]&][[;;,3]]],{n,0,70}] (* _Harvey P. Dale_, Apr 13 2025 *)
%Y A326461 Cf. A010051, A259198, A326455, A326456, A326457, A326458, A326459, A326460, A326462, A326463.
%K A326461 nonn
%O A326461 0,17
%A A326461 _Wesley Ivan Hurt_, Jul 06 2019