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%I #26 Jul 07 2019 07:46:34
%S 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 43,53,48,65,56,77,66,85,77,104,84,118,99,133,112,155,123,177,143,196,
%U 162,227,174,256,200,282,220,318,241,360,270,389,300,442,322
%N Number of partitions of n into eight primes.
%H Alois P. Heinz, <a href="/A259198/b259198.txt">Table of n, a(n) for n = 16..10000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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 a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%F a(n) = A326455(n)/n for n > 0. - _Wesley Ivan Hurt_, Jul 06 2019
%e 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].
%Y Column k=8 of A117278.
%Y Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, A259196, A259197, this sequence, A259200, A259201.
%Y Cf. A000040.
%K nonn,easy
%O 16,4
%A _Doug Bell_, Jun 20 2015
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