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A027341
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Number of partitions of n that do not contain 7 as a part.
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2
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1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 70, 90, 120, 154, 201, 255, 329, 413, 526, 657, 826, 1024, 1278, 1573, 1946, 2383, 2926, 3563, 4349, 5267, 6391, 7707, 9300, 11165, 13412, 16033, 19173, 22836, 27195, 32273, 38291, 45284, 53538, 63119, 74373
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1-x^7) Product_{m>0} 1/(1-x^m).
a(n) ~ 7*Pi * exp(sqrt(2*n/3)*Pi) / (12*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 7*Pi/(2*sqrt(6)))/sqrt(n) + (85/8 + 9/(2*Pi^2) + 9577*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016
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MATHEMATICA
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Table[Count[IntegerPartitions[n], _?(FreeQ[#, 7]&)], {n, 0, 50}] (* Harvey P. Dale, Sep 26 2021 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff((1-x^7)/eta(x+x*O(x^n)), n))
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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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