%I #5 Jul 13 2019 09:11:23

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,3,5,6,8,14,14,19,26,31,38,46,

%T 53,62,81,86,105,119,140,162,204,205,263,275,341,356,452,435,562,559,

%U 700,709,904,829,1101,1060,1343,1272,1643,1485,1982,1795,2318

%N Sum of the second 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)} A010051(q) * A010051(p) * A010051(o) * A010051(m) * A010051(l) * A010051(k) * A010051(j) * A010051(i) * A010051(n-i-j-k-l-m-o-p-q) * i.

%F a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326549(n).

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[m] - PrimePi[m - 1]) (PrimePi[o] - PrimePi[o - 1]) (PrimePi[p] - PrimePi[p - 1]) (PrimePi[q] - PrimePi[q - 1]) (PrimePi[n - i - j - k - l - m - o - p - q] - PrimePi[n - i - j - k - l - m - o - p - q - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

%Y Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326545, A326546, A326547, A326549.

%K nonn

%O 0,19

%A _Wesley Ivan Hurt_, Jul 13 2019