Search: id:A105479
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%I A105479
%S A105479 0,0,1,3,12,50,225,1092,5684,31572,186300,1163085,7654350,52928460,
%T A105479 383437327,2902665885,22907918640,188082362120,1603461748491,
%U A105479 14169892736484,129594593170210,1224875863061970,11948280552370932
%N A105479 a(n) = C(n,2)*Bell(n-2) (cf. A000217, A000110).
%C A105479 Number of blocks of size 2 in all set partitions of {1,2,...,n}. Example: 
               a(3)=3 because the set partitions of {1,2,3} are 1|2|3, 1|23, 12|3, 
               13|2 and 123, containing exactly 3 blocks of size 2. a(n)=Sum(k*A124498(n-1,
               k), k>=0}. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 06 2006
%C A105479 Number of partitions of {1...n} containing 2 pairs of consecutive integers, 
               where each pair is counted within a block and a string of more than 
               2 consecutive integers are counted two at a time. E.g. a(4) = 3 because 
               the partitions of {1,2,3,4} with 2 pairs of consecutive integers 
               are 123/4,12/34,1/234. - A. O. Munagi (amunagi(AT)yahoo.com), Apr 
               10 2005
%D A105479 A. O. Munagi, Set Partitions with Successions and Separations, Int. J. 
               Math and Math. Sc. 2005, no. 3 (2005), 451-463.
%H A105479 A. O. Munagi, <a href="http://www.emis.de/journals/HOA/IJMMS/2005/3451.pdf">
               Set Partitions with Successions and Separations</a>,IJMMS 2005:3 
               (2005),451-463.
%F A105479 a(n) = binomial(n-1, 2)*Bell(n-3), the case r = 2 of the general case 
               of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1).
%F A105479 E.g.f.: z^2/2 * e^(e^z-1) - Frank Ruskey (ruskey(AT)cs.uvic.ca), Dec 
               26 2006
%F A105479 G.f.: exp(-1)*Sum(x^2/(n!*(1-n*x)^3),n=0..infinity). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Feb 05 2008
%p A105479 [seq(binomial(n,2)*combinat[bell](n-2),n=0..50)];
%Y A105479 Cf. A105480, A105489, A105484, A124498.
%Y A105479 Sequence in context: A074547 A151178 A151179 this_sequence A151180 A151181 
               A094601
%Y A105479 Adjacent sequences: A105476 A105477 A105478 this_sequence A105480 A105481 
               A105482
%K A105479 easy,nonn
%O A105479 0,4
%A A105479 A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
%E A105479 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 01 2007

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