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A109703
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Number of partitions of n into parts each equal to 1 mod 7.
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8
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1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 7, 7, 7, 7, 7, 8, 10, 11, 12, 12, 12, 12, 13, 15, 17, 18, 19, 19, 19, 20, 23, 26, 28, 29, 30, 30, 31, 34, 38, 41, 43, 44, 45, 46, 50, 55, 60, 63, 65, 66, 68, 72, 79, 85, 90, 93, 95, 97, 103, 111, 120, 127, 132, 135
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f.: 1/product(1-x^(1+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006
a(n) ~ Gamma(1/7) * exp(Pi*sqrt(2*n/21)) / (2^(11/7) * 3^(1/14) * 7^(3/7) * Pi^(6/7) * n^(4/7)) * (1 - (2*sqrt(6/7)/(7*Pi) + 13*Pi/(168*sqrt(42))) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
G.f.: Sum_{k>=0} x^k / Product_{j=1..k} (1 - x^(7*j)). - Ilya Gutkovskiy, Jul 17 2019
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EXAMPLE
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a(15)=3 because we have 15=8+1+1+1+1+1+1+1=1+1+1+1+1+1+1+1+1+1+1+1+1+1+1.
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MAPLE
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g:=1/product(1-x^(1+7*j), j=0..20): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=0..77); # Emeric Deutsch, Apr 14 2006
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MATHEMATICA
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nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+1)), {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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