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A184176
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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)).
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3
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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
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=0..50.
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FORMULA
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T(n,k) = Sum((-1)^{k+j} * C(j,k) * C(n-2j,j) * bell(n-3j), j=k..floor(n/3)).
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EXAMPLE
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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;
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MAPLE
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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
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CROSSREFS
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Cf. A000110, A052889, A184174, A184175, A184177.
Sequence in context: A030730 A117131 A204117 * A163546 A172385 A224783
Adjacent sequences: A184173 A184174 A184175 * A184177 A184178 A184179
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch, Feb 09 2011
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STATUS
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approved
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