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Search: id:A117930
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| A117930 |
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Number of partitions of 2n into factorial parts (0! not allowed, i.e. only one kind of 1 can be a part). Also number of partitions of 2n+1 into factorial parts. |
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+0
1
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| 1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 36, 42, 48, 56, 64, 72, 82, 92, 102, 114, 126, 138, 153, 168, 183, 201, 219, 237, 258, 279, 300, 324, 348, 372, 400, 428, 456, 488, 520, 552, 588, 624, 660, 700, 740, 780, 825, 870, 915, 965, 1015, 1065, 1120, 1175, 1230
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A064986(2n)=A064986(2n+1). The first 48 terms of this sequence agree with those of A090632.
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FORMULA
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G.f.=1/[(1-x)*product(1-x^(j!/2)], j=2..infinity).
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EXAMPLE
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a(3)=5 because the partitions of 6 into factorials are [6],[2,2,2],[2,2,1,1],[2,1,1,1,1] and [1,1,1,1,1,1].
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MAPLE
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g:=1/(1-x)/product(1-x^(j!/2), j=2..7): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..65);
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CROSSREFS
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Cf. A064986, A090632.
Sequence in context: A130206 A022794 A025693 this_sequence A090632 A022786 A005704
Adjacent sequences: A117927 A117928 A117929 this_sequence A117931 A117932 A117933
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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EXTENSIONS
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An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009
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