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 A308856 #10 Oct 01 2021 15:40:17
%S A308856 0,0,0,0,0,0,0,0,0,0,2,2,2,4,5,7,7,7,8,12,10,14,18,20,18,29,21,32,28,
%T A308856 37,38,56,34,59,47,72,51,85,55,101,68,112,81,139,73,151,105,179,110,
%U A308856 209,113,244,136,258,161,323,147,354,187,387,200,436,204,501
%N A308856 Sum of the fourth largest parts in the partitions of n into 5 primes.
%H A308856 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308856 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l) * k, where c = A010051.
%F A308856 a(n) = A308854(n) - A308855(n) - A308857(n) - A308858(n) - A308859(n).
%t A308856 Table[Sum[Sum[Sum[Sum[k (PrimePi[l] - PrimePi[l - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k - l] - PrimePi[n - i - j - k - l - 1]), {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]
%Y A308856 Cf. A010051, A259195, A308854, A308855, A308857, A308858, A308859.
%K A308856 nonn
%O A308856 0,11
%A A308856 _Wesley Ivan Hurt_, Jun 28 2019