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A009714
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a(n) = Product_{i=0..8} floor((n+i)/9).
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10
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 768, 1152, 1728, 2592, 3888, 5832, 8748, 13122, 19683, 26244, 34992, 46656, 62208, 82944, 110592, 147456, 196608, 262144, 327680, 409600, 512000, 640000, 800000, 1000000, 1250000, 1562500
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OFFSET
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0,11
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COMMENTS
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For n >= 9, a(n) is the maximal product of 9 positive integers with sum n. - Wesley Ivan Hurt, Jul 08 2022
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 8, -16, 8, 0, 0, 0, 0, 0, 0, -28, 56, -28, 0, 0, 0, 0, 0, 0, 56, -112, 56, 0, 0, 0, 0, 0, 0, -70, 140, -70, 0, 0, 0, 0, 0, 0, 56, -112, 56, 0, 0, 0, 0, 0, 0, -28, 56, -28, 0, 0, 0, 0, 0, 0, 8, -16, 8, 0, 0, 0, 0, 0, 0, -1, 2, -1).
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FORMULA
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a(9*n+j) = n^(9-j)*(n+1)^j for 0 <= j <= 8. - Robert Israel, Nov 21 2022
Sum_{n>=9} 1/a(n) = 1 + zeta(9). - Amiram Eldar, Jan 10 2023
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PROG
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(PARI) a(n) = prod(k=0, 8, floor((n+k)/9)); \\ Georg Fischer, Nov 07 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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