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A001659
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Expansion of bracket function.
(Formerly M1433 N0567)
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8
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1, 1, -1, 2, -5, 13, -33, 80, -184, 402, -840, 1699, -3382, 6750, -13716, 28550, -60587, 129579, -275915, 579828, -1197649, 2431775, -4870105, 9672634, -19173013, 38151533, -76521331, 154941608, -316399235, 649807589, -1337598675, 2751021907, -5640238583, 11513062785, -23389948481, 47310801199, -95345789479, 191616365385
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OFFSET
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1,4
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COMMENTS
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Inverse binomial transform of A006218.
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} ((-1)^(n-j)*binomial(n,j)*Sum_{k=1..j} floor(j/k)).
G.f.: Sum_{k>0} x^k/((1+x)^k-x^k).
G.f.: Sum_{n>=1} z^n/(1-z^n) (Lambert series) where z=x/(1+x). - Joerg Arndt, Jan 30 2011
a(n) = Sum_{k=1..n} (-1)^(n-k)*binomial(n-1,k-1)*tau(k). - Ridouane Oudra, Aug 21 2021
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MATHEMATICA
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Table[Sum[(-1)^(n - k)*Binomial[n, k]*Sum[Floor[k/j], {j, 1, k}], {k, 0, n}], {n, 1, 50}] (* G. C. Greubel, Jul 02 2017 *)
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PROG
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(PARI) a(n)=sum(j=0, n, (-1)^(n-j)*binomial(n, j)*sum(k=1, j, j\k))
(PARI) a(n)=polcoeff(sum(k=1, n, x^k/((1+x)^k-x^k), x*O(x^n)), n)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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