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 A177257 a(n) = Sum((binomial(n,j)-j-1)*B(j), j=0..n-1), where B(j)=A000110(j) are the Bell numbers. 4
 0, 0, 0, 1, 8, 47, 258, 1426, 8154, 48715, 305012, 2001719, 13754692, 98801976, 740584196, 5782218745, 46942426080, 395607218279, 3455493024350, 31236784338746, 291836182128670, 2814329123555051, 27980637362452980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 MAPLE 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); MATHEMATICA Table[Sum[(Binomial[n, j]-j-1)BellB[j], {j, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Oct 15 2015 *) CROSSREFS Cf. A000110, A005493, A177254, A177255, A177256. Sequence in context: A026900 A016198 A270495 * A051140 A296631 A255720 Adjacent sequences: A177254 A177255 A177256 * A177258 A177259 A177260 KEYWORD nonn AUTHOR Emeric Deutsch, May 07 2010 STATUS approved

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Last modified April 1 12:16 EDT 2023. Contains 361691 sequences. (Running on oeis4.)