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%I #9 May 07 2022 20:59:11
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,8,8,11,15,15,19,22,
%T 24,26,34,36,44,47,53,59,73,71,87,93,109,109,138,128,163,157,190,190,
%U 238,210,277,262,325,300,387,344,457,399,515,464,617,515
%N Sum of the eighth largest parts of the partitions of n into 9 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} 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) * p, where c = A010051.
%F a(n) = A326540(n) - A326541(n) - A326543(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).
%t Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,PrimeQ]&][[All,8]]],{n,0,70}] (* _Harvey P. Dale_, May 03 2022 *)
%Y Cf. A010051, A259200, A326540, A326541, A326543, A326544, A326545, A326546, A326547, A326548, A326549.
%K nonn
%O 0,19
%A _Wesley Ivan Hurt_, Jul 13 2019