Search: id:A105480 Results 1-1 of 1 results found. %I A105480 %S A105480 1,4,20,100,525,2912,17052,105240,683100,4652340,33168850,246999480, %T A105480 1917186635,15480884720,129811538960,1128494172720,10155257740443, %U A105480 94465951576560,907162152191470,8982422995787780,91603484234843812 %N A105480 Number of partitions of {1...n} containing 3 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. %D A105480 A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463. %H A105480 A. O. Munagi, Set partitions with successions and separations, Int. J. Math. Math. Sci. (IJMMS) vol 2005 no 3 (2005) pp 451-463. %F A105480 a(n) = binomial(n-1, 3)Bell(n-4), the case r = 3 in the general case of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1). %F A105480 O.g.f. for c(n,r) is exp(-1)*Sum(x^(r+1)/(n!*(1-n*x)^(r+1)),n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008 %e A105480 a(5) = 4 because the partitions of {1,2,3,4,5} with 3 pairs of consecutive integers are 1234/5,123/45,12/345,1/2345. %p A105480 seq(binomial(n-1,3)*combinat[bell](n-4),n=4..25); %Y A105480 Cf. A105479, A105481, A105485, A105490. %Y A105480 Sequence in context: A073532 A103771 A005054 this_sequence A155485 A155181 A082761 %Y A105480 Adjacent sequences: A105477 A105478 A105479 this_sequence A105481 A105482 A105483 %K A105480 easy,nonn %O A105480 4,2 %A A105480 A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005 Search completed in 0.001 seconds