Search: id:A007837
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%I A007837
%S A007837 1,1,4,5,16,82,169,541,2272,17966,44419,201830,802751,4897453,
%T A007837 52275409,166257661,840363296,4321172134,24358246735,183351656650,
%U A007837 2762567051857,10112898715063,62269802986835,343651382271526
%N A007837 Number of partitions of n-set with distinct block sizes.
%D A007837 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
%H A007837 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. <a href="http://www.combinatorics.org/
               ">Electron. J. Combin.</a>, 6 (1999), no. 1, Research Paper 2, 36 
               pp.
%F A007837 E.g.f.: Product {m >= 1} (1+x^m/m!)
%F A007837 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
%p A007837 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]
%Y A007837 Cf. A007838.
%Y A007837 Sequence in context: A110278 A013628 A127007 this_sequence A032219 A032144 
               A032049
%Y A007837 Adjacent sequences: A007834 A007835 A007836 this_sequence A007838 A007839 
               A007840
%K A007837 nonn
%O A007837 1,3
%A A007837 Arnold Knopfmacher (ARNOLDK(AT)gauss.cam.wits.ac.za)
%E A007837 More terms from Christian G. Bower (bowerc(AT)usa.net)

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