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A103264
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Number of partitions of n into distinct parts prime to 3, 5 and 7.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 23, 24, 26, 28, 31, 34, 37, 39, 42, 45, 49, 53, 56, 60, 64, 69, 75, 81, 86, 92, 98, 105, 113, 122, 130, 138, 147, 157, 168, 179, 191, 202, 215, 230, 246, 262, 279
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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FORMULA
| G.f.: product_{k>0}((1+x^k)*(1+x^(15k))*(1+x^(21k))*(1+x^(35k)))/((1+x^(3k))*(1+x^(5k))*(1+x^(7k))*(1+x^(105k))).
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EXAMPLE
| E.g. a(19)=5 because 19=17+2=16+2+1=13+4+2=11+8.
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MAPLE
| series(product((1+x^k)*(1+x^(15*k))*(1+x^(21*k))*(1+x^(35*k)))/((1+x^(3*k))*(1+x^(5*k))*(1+x^(7*k))*(1+x^(105*k))), k=1..100), x=0, 100);
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MATHEMATICA
| CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15k))(1 + x^(21k))(1 + x^(35k))/((1 + x^(3k))(1 + x^(5k))(1 + x^(7k))(1 + x^(105k))), {k, 100}], {x, 0, 73}], x] (from Robert G. Wilson v Feb 22 2005)
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CROSSREFS
| Sequence in context: A048688 A092695 A033270 * A060960 A073642 A108356
Adjacent sequences: A103261 A103262 A103263 * A103265 A103266 A103267
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Feb 21 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005
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