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A259201
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Number of partitions of n into ten primes.
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23
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1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 11, 11, 14, 16, 18, 20, 25, 24, 31, 33, 38, 39, 48, 47, 59, 59, 69, 69, 87, 80, 102, 98, 118, 114, 143, 131, 168, 154, 191, 179, 227, 200, 261, 236, 297, 268, 344, 300, 396, 345, 442, 390, 509, 431, 576, 493, 641, 551, 729
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OFFSET
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20,4
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LINKS
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FORMULA
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a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019
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)} A010051(r) * 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-r). - Wesley Ivan Hurt, Jul 13 2019
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EXAMPLE
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a(23) = 2 because there are 2 partitions of 23 into ten primes: [2,2,2,2,2,2,2,2,2,5] and [2,2,2,2,2,2,2,3,3,3].
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PROG
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(Magma) [#RestrictedPartitions(k, 10, Set(PrimesUpTo(1000))):k in [20..80]] ; // Marius A. Burtea, Jul 13 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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