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A177257
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a(n) = Sum_{j=0..n-1} (binomial(n,j) - (j+1))*A000110(j).
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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.
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n-1} (binomial(n,j) - (j+1))*Bell(j), where Bell(n) = A000110(n) are the Bell numbers.
a(n) = Sum_{k=0..floor(n/2)} k*A177256(n,k).
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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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PROG
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(Magma)
A177257:= func< n | n eq 0 select 0 else (&+[(Binomial(n, j)-(j+1))*Bell(j): j in [0..n-1]]) >;
(SageMath)
def A177257(n): return sum((binomial(n, j) -(j+1))*bell_number(j) for j in range(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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