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A177257
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a(n) = Sum((binomial(n,j)-j-1)*B(j), j=0..n-1), where B(j)=A000110(j) are the Bell numbers.
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4
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0, 0, 0, 1, 8, 47, 258, 1426, 8154, 48715, 305012, 2001719, 13754692, 98801976, 740584196, 5782218745, 46942426080, 395607218279, 3455493024350, 31236784338746, 291836182128670, 2814329123555051, 27980637362452980
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OFFSET
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0,5
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COMMENTS
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Number of blocks not consisting of consecutive integers in all partitions of the set {1,2,...,n} (a singleton is considered a block of consecutive integers). Example: a(3)=1 because in 1-2-3, 1-23, 12-3, 13-2, and 123 only the block 13 does not consist of consecutive integers.
a(n) = Sum(k*A(177256(n,k), k=0..floor(n/2)).
a(n) = A005493(n-1)-A177255(n).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..500
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MAPLE
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with(combinat): a:= proc(n) add((binomial(n, j)-j-1)*bell(j), j = 0 .. n-1) end proc: seq(a(n), n = 0 .. 22);
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MATHEMATICA
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Table[Sum[(Binomial[n, j]-j-1)BellB[j], {j, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Oct 15 2015 *)
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CROSSREFS
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Cf. A000110, A005493, A177254, A177255, A177256.
Sequence in context: A026900 A016198 A270495 * A051140 A296631 A255720
Adjacent sequences: A177254 A177255 A177256 * A177258 A177259 A177260
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, May 07 2010
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STATUS
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approved
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