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 A259198 #30 Apr 26 2025 08:28:16
%S A259198 1,1,1,2,2,3,4,4,5,6,7,8,10,9,12,14,16,16,21,19,26,26,31,30,39,34,46,
%T A259198 43,53,48,65,56,77,66,85,77,104,84,118,99,133,112,155,123,177,143,196,
%U A259198 162,227,174,256,200,282,220,318,241,360,270,389,300,442,322
%N A259198 Number of partitions of n into eight primes.
%H A259198 Alois P. Heinz, <a href="/A259198/b259198.txt">Table of n, a(n) for n = 16..10000</a>
%H A259198 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A259198 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)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(p) * A010051(n-i-j-k-l-m-o-p). - _Wesley Ivan Hurt_, Apr 17 2019
%F A259198 a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%F A259198 a(n) = A326455(n)/n for n > 0. - _Wesley Ivan Hurt_, Jul 06 2019
%e A259198 a(20) = 2 because there are 2 partitions of 20 into eight primes: [2,2,2,2,2,2,3,5] and [2,2,2,2,3,3,3,3].
%t A259198 Table[Length@IntegerPartitions[n, {8}, Prime@Range@100], {n, 16, 100}] (* _Robert Price_, Apr 25 2025 *)
%Y A259198 Column k=8 of A117278.
%Y A259198 Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, A259196, A259197, this sequence, A259200, A259201.
%Y A259198 Cf. A000040.
%K A259198 nonn,easy
%O A259198 16,4
%A A259198 _Doug Bell_, Jun 20 2015