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%I #9 Sep 17 2021 17:59:32
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,8,8,10,15,17,19,
%T 23,24,30,34,38,44,54,53,67,73,83,87,105,107,131,136,156,161,200,186,
%U 233,232,275,271,335,315,398,373,456,439,550,493,636,589
%N Sum of the ninth largest parts of the partitions of n into 10 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} c(r) * c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q-r) * q, where c = A010051.
%F a(n) = A326678(n) - A326679(n) - A326681(n) - A326682(n) - A326683(n) - A326684(n) - A326685(n) - A326686(n) - A326687(n) - A326688(n).
%t Table[Total[Select[IntegerPartitions[n,{10}],AllTrue[#,PrimeQ]&][[All,9]]],{n,0,70}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 01 2019 *)
%Y Cf. A010051, A259201, A326678, A326679, A326681, A326682, A326683, A326684, A326685, A326686, A326687, A326688.
%K nonn
%O 0,21
%A _Wesley Ivan Hurt_, Jul 17 2019
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