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A002774
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Number of bipartite partitions of n white objects and n black ones.
(Formerly M1925 N0760)
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5
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1, 2, 9, 31, 109, 339, 1043, 2998, 8406, 22652, 59521, 151958, 379693, 927622, 2224235, 5236586, 12130780, 27669593, 62229990, 138095696, 302673029, 655627975, 1404599867, 2977831389, 6251060785, 12999299705, 26791990052
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of ways to factor p^n*q^n where p and q are distinct primes.
a(n) = A054225(n,n). [Reinhard Zumkeller, Nov 30 2011]
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REFERENCES
| F. C. Auluck, On partitions of bipartite numbers. Proc. Cambridge Philos. Soc. 49, (1953). 72-83.
M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 1.
A. Murthy, Generalization of partition function, introducing Smarandache factor partitions. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000.
A. Murthy, Program for finding out the number of Smarandache factor partitions. (To be published in Smarandache Notions Journal).
Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 1.4, 1.14.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| M. L. Perez et al., eds., Smarandache Notions Journal
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FORMULA
| a(n) = A054225(2n, n) = A091437(2n).
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MATHEMATICA
| max = 26; se = Series[ Sum[ Log[1 - x^(n-k)*y^k], {n, 1, 2max}, {k, 0, n}], {x, 0, 2max}, {y, 0, 2max}]; coes = CoefficientList[ Series[ Exp[-se], {x, 0, 2max}, {y, 0, 2max}], {x, y}]; a[n_] := coes[[n+1, n+1]]; Table[a[n], {n, 0, max} ](* From Jean-François Alcover, Dec 06 2011 *)
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CROSSREFS
| Cf. A005380.
Sequence in context: A151823 A084652 A188776 * A150905 A150906 A150907
Adjacent sequences: A002771 A002772 A002773 * A002775 A002776 A002777
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected using A000491.
Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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