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 A168605 Number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly three nonempty parts. 3
 1, 2, 8, 30, 104, 342, 1088, 3390, 10424, 31782, 96368, 291150, 877544, 2640822, 7938848, 23849310, 71613464, 214971462, 645176528, 1936053870, 5809210184, 17429727702, 52293377408, 156888520830, 470682339704, 1412080573542 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5 Index entries for linear recurrences with constant coefficients, signature (6,-11,6). FORMULA a(3)=1 and, for n>=4, a(n)=(5*3^(n-3)-3*2^(n-2)+3)/3. The shifted e.g.f. is (5e^(3x)-6e^(2x)+3e^x+1)/3. G.f.: x^3(1-4x+7x^2-2x^3)/((1-x)(1-2x)(1-3x)). MATHEMATICA f5[n_] := (5 3^(n - 3) - 3 2^(n - 2) + 3)/3; Table[f5[n], {n, 4, 28}] CROSSREFS The number of ways of partitioning the multiset {1, 1, 1, 2, 3, ..., n-1} into exactly two and four nonempty parts are given in A168604 and A168606, respectively. Sequence in context: A010749 A299415 A230701 * A127865 A199923 A230269 Adjacent sequences:  A168602 A168603 A168604 * A168606 A168607 A168608 KEYWORD nonn,easy AUTHOR Martin Griffiths, Dec 01 2009 EXTENSIONS Last element of the multiset in the definition corrected by Martin Griffiths, Dec 02 2009 STATUS approved

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)