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A326597
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Sum of the second largest parts of the partitions of n into 10 parts.
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10
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 91, 137, 190, 277, 376, 525, 704, 956, 1255, 1671, 2160, 2818, 3599, 4616, 5819, 7369, 9187, 11480, 14179, 17527, 21441, 26256, 31851, 38649, 46543, 56022, 66980, 80050, 95083, 112860, 133266
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OFFSET
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0,13
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LINKS
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FORMULA
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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)} i.
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MATHEMATICA
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Table[Total[IntegerPartitions[n, {10}][[;; , 2]]], {n, 0, 50}] (* Harvey P. Dale, Nov 19 2023 *)
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CROSSREFS
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Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326598.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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