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Search: id:A054440
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| A054440 |
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Number of ordered pairs of partitions of n with no common parts. |
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+0
1
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| 1, 0, 2, 4, 12, 16, 48, 60, 148, 220, 438, 618, 1302, 1740, 3216, 4788, 8170, 11512, 19862, 27570, 45448, 64600, 100808, 141724, 223080, 307512, 465736, 652518, 968180, 1334030, 1972164, 2691132, 3902432, 5347176, 7611484, 10358426
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Corteel, Sylvie; Savage, Carla D.; Wilf, Herbert S.; Zeilberger, Doron, A pentagonal number sieve. J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192.
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LINKS
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H. S. Wilf, A pentagonal number sieve (with Sylvie Corteel, Carla Savage and Doron Zeilberger)
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FORMULA
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G.f.: Sum[p(n)^2x^n]/Sum[p(n)x^n] (p(n)=number of partitions of n)
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EXAMPLE
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a(3)=4 because of the 4 pairs of partitions of 3: (3,21),(3,111),(21,3),(111,3)
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MAPLE
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with(combinat): p1 := sum(numbpart(n)^2*x^n, n=0..500): it := p1*product((1-x^i), i=1..500): s := series(it, x, 500): for i from 0 to 100 do printf(`%d, `, coeff(s, x, i)) od:
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CROSSREFS
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Sequence in context: A071118 A132314 A053636 this_sequence A074646 A097001 A085931
Adjacent sequences: A054437 A054438 A054439 this_sequence A054441 A054442 A054443
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KEYWORD
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easy,nonn
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AUTHOR
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Herbert Wilf (wilf(AT)math.upenn.edu), May 13 2000
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EXTENSIONS
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Corrected and extended by James A. Sellers (sellersj(AT)math.psu.edu), May 23 2000
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