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 A307637 #47 Oct 28 2022 04:21:53
%S A307637 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,3,5,6,8,14,14,16,23,28,35,38,45,52,
%T A307637 71,66,85,94,115,121,163,154,212,194,260,253,344,289,411,382,516,457,
%U A307637 640,533,786,652,914,778,1112,857,1299,1048,1501,1195,1780,1345
%N A307637 Sum of the second largest parts of the partitions of n into 7 primes.
%H A307637 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A307637 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o) * i, where c = A010051.
%F A307637 a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308978(n) - A308979(n) - A308980(n).
%t A307637 Table[Total[Select[IntegerPartitions[n,{7}],AllTrue[#,PrimeQ]&][[All,2]]],{n,0,60}] (* _Harvey P. Dale_, Oct 23 2022 *)
%Y A307637 Cf. A010051, A259197, A308974, A308975, A308976, A308977, A308978, A308979, A308980.
%K A307637 nonn
%O A307637 0,15
%A A307637 _Wesley Ivan Hurt_, Jul 04 2019