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Search: id:A052335
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| A052335 |
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Number of partitions of n into at most 1 copy of 1, 2 copies of 2, 3 copies of 3,... |
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+0
4
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| 1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 17, 22, 28, 36, 46, 58, 73, 91, 114, 141, 173, 213, 261, 318, 387, 469, 567, 683, 821, 984, 1176, 1403, 1671, 1984, 2351, 2781, 3284, 3869, 4550, 5343, 6264, 7330, 8565, 9993, 11642, 13543, 15733, 18252, 21148, 24471
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also number of partitions into non pronic numbers (cannot be written as i*(i+1)).
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 0..128 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 13 2009]
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FORMULA
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G.f.: prod( (1-x^(i*(i+1)))/(1-x^i), i=1..infinity )
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EXAMPLE
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a(5)=4 because we have [5],[4,1],[3,2] and [2,2,1] ([3,1,1],[2,1,1,1] and [1,1,1,1,1] do not qualify).
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MAPLE
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g:=product((1-x^(j*(j+1)))/(1-x^j), j=1..53): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=0..49); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2006
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CROSSREFS
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Cf. A000009, A000041, A002378.
Sequence in context: A036034 A006950 A106507 this_sequence A160333 A136422 A018127
Adjacent sequences: A052332 A052333 A052334 this_sequence A052336 A052337 A052338
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Dec 19 1999
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