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A089353
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Triangle read by rows: T(n,m) = number of planar partitions of n with trace m.
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2
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1, 2, 1, 3, 2, 1, 4, 6, 2, 1, 5, 10, 6, 2, 1, 6, 19, 14, 6, 2, 1, 7, 28, 28, 14, 6, 2, 1, 8, 44, 52, 33, 14, 6, 2, 1, 9, 60, 93, 64, 33, 14, 6, 2, 1, 10, 85, 152, 127, 70, 33, 14, 6, 2, 1, 11, 110, 242, 228, 142, 70, 33, 14, 6, 2, 1, 12, 146, 370, 404, 272, 149, 70, 33, 14, 6, 2, 1, 13
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also number of partitions of n objects of 2 colors into k parts, each part containing at least one black object.
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REFERENCES
| G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (Ch. XI, exercise 5 and Ch. XII, exercise 5).
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FORMULA
| G.f.: Prod(k=1..oo, 1/(1-q x^k)^k).
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EXAMPLE
| 1; 2,1; 3,2,1; 4,6,2,1; 5,10,6,2,1; 6,19,14,6,2,1; ...
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CROSSREFS
| Cf. A000219 (row sums), A005380, A005993 (trace 2), A050531 (trace 3), A089351 (trace 4).
Sequence in context: A104741 A167237 A200154 * A136451 A066121 A039911
Adjacent sequences: A089350 A089351 A089352 * A089354 A089355 A089356
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KEYWORD
| nonn,tabl
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AUTHOR
| Wouter Meeussen and Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 26 2003
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EXTENSIONS
| Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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