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A143862
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Number of compositions of n such that every part is divisible by number of parts.
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10
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1, 1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 9, 1, 7, 7, 9, 1, 19, 1, 14, 16, 11, 1, 43, 2, 13, 29, 34, 1, 56, 1, 51, 46, 17, 16, 130, 1, 19, 67, 139, 1, 105, 1, 142, 162, 23, 1, 315, 2, 151, 121, 246, 1, 219, 211, 321, 154, 29, 1, 1021, 1, 31, 219, 488, 496, 495, 1, 594, 232, 834, 1, 1439, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} x^(k^2) / (1 - x^k)^k.
G.f.: 1 + Sum_{n>=1} (1 + x^n)^(n-1) * x^n. - Paul D. Hanna, Jul 09 2019
a(n) = Sum_{d|n} binomial(n/d-1, d-1) for n>0 with a(0) = 1. - Paul D. Hanna, Apr 25 2018
G.f.: 1 + Sum_{n>=1} (x^n/(1-x^n))^n (conjecture). - Joerg Arndt, Jan 04 2024
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PROG
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(PARI) {a(n) = if(n==0, 1, sumdiv(n, d, binomial(n/d-1, d-1) ))}
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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