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A109707
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Number of partitions of n into parts each equal to 5 mod 7.
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4
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1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 2, 1, 3, 1, 3, 2, 2, 3, 1, 4, 2, 4, 3, 2, 5, 2, 6, 3, 5, 5, 3, 7, 3, 8, 5, 6, 8, 4, 10, 5, 10, 8, 8, 11, 6, 13, 8, 13, 12, 10, 15, 9, 18, 12, 17, 16, 14, 21, 13, 23, 17, 22, 23, 18, 28, 18, 31, 24, 28
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OFFSET
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0,25
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LINKS
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FORMULA
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G.f.: 1/product(1-x^(5+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006
a(n) ~ Gamma(5/7) * exp(Pi*sqrt(2*n/21)) / (2^(13/7) * 3^(5/14) * 7^(1/7) * Pi^(2/7) * n^(6/7)) * (1 + (11*Pi/(168*sqrt(42)) - 15*sqrt(6/7)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
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EXAMPLE
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a(36)=3 because we have 36=26+5+5=19+12+5=12+12+12.
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MAPLE
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g:=1/product(1-x^(5+7*j), j=0..20): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..92); # Emeric Deutsch, Apr 14 2006
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MATHEMATICA
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nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+5)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)
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CROSSREFS
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KEYWORD
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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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