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 A259197 #29 Apr 26 2025 08:27:59
%S A259197 1,1,1,2,2,3,4,4,4,6,6,8,8,9,10,14,12,16,16,19,19,26,22,30,26,34,31,
%T A259197 43,33,48,42,56,47,66,51,77,60,84,68,99,73,112,86,123,95,143,103,162,
%U A259197 116,174,131,200,137,220,156,241,171,270,180,300,202,322,223,359
%N A259197 Number of partitions of n into seven primes.
%H A259197 Alois P. Heinz, <a href="/A259197/b259197.txt">Table of n, a(n) for n = 14..10000</a>
%H A259197 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A259197 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)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(n-i-j-k-l-m-o). - _Wesley Ivan Hurt_, Apr 17 2019
%F A259197 a(n) = [x^n y^7] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%e A259197 a(17) = 2 because there are 2 partitions of 17 into seven primes: [2,2,2,2,2,2,5] and [2,2,2,2,3,3,3].
%t A259197 Table[Length@IntegerPartitions[n, {7}, Prime@Range@100], {n, 14, 100}] (* _Robert Price_, Apr 25 2025 *)
%Y A259197 Column k=7 of A117278.
%Y A259197 Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, A259196, this sequence, A259198, A259200, A259201.
%Y A259197 Cf. A000040.
%K A259197 nonn,easy
%O A259197 14,4
%A A259197 _Doug Bell_, Jun 20 2015