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A147654
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Result of using the positive integers 1,2,3,... as coefficients in an infinite polynomial series in x and then expressing this series as Product_{k>=1} (1+a(k)x^k).
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10
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1, 2, 1, 3, 0, -2, 0, 9, 0, -6, 0, 4, 0, -18, 0, 93, 0, -54, 0, 72, 0, -186, 0, 232, 0, -630, 0, 1020, 0, -2106, 0, 10881, 0, -7710, 0, 13824, 0, -27594, 0, 49440, 0, -97902, 0, 191844, 0, -364722, 0, 590800, 0, -1340622, 0, 2656920, 0, -4918482, 0, 9791784, 0, -18512790
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OFFSET
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1,2
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LINKS
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FORMULA
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Product_{k>=1} (1+a(k)*x^k) = 1 + Sum_{k>=1} k*x^k. - Seiichi Manyama, Jun 24 2018
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EXAMPLE
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From the positive integers 1,2,3,..., construct the series 1+x+2x^2+3x^3+4x^4+... a(1) is always the coefficient of x, here 1. Divide by (1+a(1)x), i.e. here (1+x), to get the quotient (1+a(2)x^2+...), which here gives a(2)=2. Then divide this quotient by (1+a(2)x^2), i.e. here (1+2x^2), to get (1+a(3)x^3+...), giving a(3)=1.
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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