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A007837
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Number of partitions of n-set with distinct block sizes.
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21
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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, 2352104168848091, 15649414071734847
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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
| Alois P. Heinz, Table of n, a(n) for n = 1..250
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
| 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
| 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); # Alois P. Heinz, Sep 06 2008
A007837 := proc(n) option remember; local k; `if`(n = 0, 1,
add(binomial(n-1, k-1) * A182927(k) * A007837(n-k), k = 1..n)) end:
seq(A007837(i), i=0..24); # - Peter Luschny, Apr 25 2011
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CROSSREFS
| Cf. A007838.
Sequence in context: A110278 A013628 A127007 * A032219 A032144 A032049
Adjacent sequences: A007834 A007835 A007836 * A007838 A007839 A007840
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KEYWORD
| nonn
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AUTHOR
| Arnold Knopfmacher (ARNOLDK(AT)gauss.cam.wits.ac.za)
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net)
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