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 A184176 Triangle read by rows: T(n,k) is the number of partitions of the set {1,2,...,n} having k adjacent blocks of size 3, i.e. blocks of the form (i,i+1,i+2) (0<=k<=floor(n/3)). 3
 1, 1, 2, 4, 1, 13, 2, 46, 6, 184, 18, 1, 805, 69, 3, 3840, 288, 12, 19775, 1324, 47, 1, 109180, 6578, 213, 4, 642382, 35136, 1032, 20, 4007712, 200398, 5390, 96, 1, 26399764, 1214136, 30027, 505, 5, 182939900, 7778856, 177744, 2792, 30, 1329327991, 52501052, 1112969, 16362, 170, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of entries in row n is 1+floor(n/3). Sum of entries in row n = A000110(n) (the Bell numbers). T(n,0) = A184177(n). Sum(k*T(n,k), k>=0) = A052889(n-2). LINKS FORMULA T(n,k) = Sum((-1)^{k+j} * C(j,k) * C(n-2j,j) * bell(n-3j), j=k..floor(n/3)). EXAMPLE T(4,1) = 2 because we have 123-4 and 1-234. Triangle starts: 1; 1; 2; 4,    1; 13,   2; 46,   6; 184, 18,  1; MAPLE with(combinat): q := 3: a := proc (n, k) options operator, arrow: sum((-1)^(k+j)*binomial(j, k)*binomial(n+j-j*q, j)*bell(n-j*q), j = k .. floor(n/q)) end proc: for n from 0 to 15 do seq(a(n, k), k = 0 .. floor(n/q)) end do; # yields sequence in triangular form CROSSREFS Cf. A000110, A052889, A184174, A184175, A184177. Sequence in context: A030730 A117131 A204117 * A163546 A172385 A224783 Adjacent sequences:  A184173 A184174 A184175 * A184177 A184178 A184179 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Feb 09 2011 STATUS approved

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