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Search: id:A002774
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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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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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Number of ways to factor p^n*q^n where p and q are distinct primes.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
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CROSSREFS
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a(n) = A060243(2n, n) = A091437(2n). Cf. A005380.
Sequence in context: A101604 A151823 A084652 this_sequence A150905 A150906 A150907
Adjacent sequences: A002771 A002772 A002773 this_sequence A002775 A002776 A002777
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected using A000491.
Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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