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Search: id:A007837
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| A007837 |
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Number of partitions of n-set with distinct block sizes. |
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+0
14
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| 1, 1, 4, 5, 16, 82, 169, 541, 2272, 17966, 44419, 201830, 802751, 4897453, 52275409, 166257661, 840363296, 4321172134, 24358246735, 183351656650, 2762567051857, 10112898715063, 62269802986835, 343651382271526
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OFFSET
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1,3
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REFERENCES
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Philippe Flajolet, Eric Fusy, Xavier Gourdon, Daniel Panario and Nicolas Pouyanne, A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, Fig. 3, arXiv:math.CO/0606370
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LINKS
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Knopfmacher, A., Odlyzko, A. M., Pittel, B., Richmond, L. B., Stark, D., Szekeres, G. and Wormald, N. C., The asymptotic number of set partitions with unequal block sizes. Electron. J. Combin., 6 (1999), no. 1, Research Paper 2, 36 pp.
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FORMULA
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E.g.f.: Product {m >= 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)*(-d!)^(-k/d) and a(0) = 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 13 2002
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MAPLE
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with (numtheory): a:= proc(n) option remember; if n=0 then 1 else add ((n-1)!/ (n-k)! *add ((-d) *(-d!)^(-k/d), d=divisors(k)) *a(n-k), k=1..n) fi end: seq (a(n), n=1..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
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CROSSREFS
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Cf. A007838.
Sequence in context: A110278 A013628 A127007 this_sequence A032219 A032144 A032049
Adjacent sequences: A007834 A007835 A007836 this_sequence A007838 A007839 A007840
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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 Christian G. Bower (bowerc(AT)usa.net)
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