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Search: id:A089333
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| A089333 |
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Number of partitions into a square number of parts. |
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+0
2
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| 1, 1, 1, 2, 2, 3, 4, 6, 8, 11, 14, 19, 24, 31, 39, 51, 63, 80, 99, 124, 153, 190, 233, 288, 353, 432, 527, 643, 780, 947, 1145, 1383, 1665, 2002, 2399, 2874, 3431, 4090, 4865, 5779, 6847, 8103, 9568, 11283, 13280, 15610, 18313, 21462, 25108, 29337, 34227
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OFFSET
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1,4
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COMMENT
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Also number of partitions of n such that the largest part is a square. Example: a(7)=4 because we have [4,3],[4,2,1],[4,1,1,1] and [1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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FORMULA
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G.f.: Sum(x^(n^2)/Product(1-x^i, i = 1 .. n^2), n = 1 .. infinity).
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EXAMPLE
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a(7)=4 because we have [7],[4,1,1,1],[3,2,1,1] and [2,2,2,1].
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MAPLE
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g:=sum(x^(k^2)/product(1-x^i, i=1..k^2), k=1..7): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=1..51); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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CROSSREFS
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Sequence in context: A035542 A130081 A141847 this_sequence A098492 A103632 A067859
Adjacent sequences: A089330 A089331 A089332 this_sequence A089334 A089335 A089336
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 25 2003
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