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Search: id:A007841
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| A007841 |
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Number of factorizations of permutations of n letters into cycles in nondecreasing length order. |
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+0
2
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| 1, 3, 11, 56, 324, 2324, 18332, 167544, 1674264, 18615432, 223686792, 2937715296, 41233157952, 623159583552, 10008728738304, 171213653641344, 3092653420877952, 59086024678203264, 1185657912197967744
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Knopfmacher, A.; Ridley, J. N.; Reciprocal sums over partitions and compositions. SIAM J. Discrete Math. 6 (1993), no. 3, 388-399.
D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388.
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FORMULA
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E.g.f.: prod{m >= 1} 1/(1-x^m/m).
a(n) = Sum_{k=1..n} (n-1)!/(n-k)!*b(k)*a(n-k), where b(k) = Sum_{d divides k} d^(1-k/d) and a(0) = 1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 14 2002
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MAPLE
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p := product(1/(1-x^m/m), m=1..100): s := series(p, x, 100): for i from 1 to 100 do printf(`%.0f, `, i!*coeff(s, x, i)) od:
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CROSSREFS
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Cf. A007837, A007838.
Adjacent sequences: A007838 A007839 A007840 this_sequence A007842 A007843 A007844
Sequence in context: A125696 A001776 A136104 this_sequence A036760 A000985 A094611
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KEYWORD
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nonn
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AUTHOR
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Arnold Knopfmacher [ ARNOLDK(AT)gauss.cam.wits.ac.za ]
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 09 2001
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