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A002051
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Differences of 0.
(Formerly M4644 N1986)
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2
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1, 9, 67, 525, 4651, 47229, 545707, 7087005, 102247051, 1622631549, 28091565547, 526858344285, 10641342962251, 230283190961469, 5315654681948587
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OFFSET
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3,2
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COMMENTS
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a(n) is the number of ways to arrange the blocks of the partitions of {1,2,...,n} in an undirected cycle of length 3 or more, see A000629. - Geoffrey Critzer, Nov 23 2012
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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).
J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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A002051(n) = A000670(n) - 2^(n-1) - Manfred Goebel (mkgoebel(AT)essex.ac.uk), Feb 20, 2000
E.g.f.: = (1 - exp(2x) - 2*Log(2 - exp(x)))/4 = B(A(x)) where A(x)=exp(x)-1 and B(x)= ( Log(1/(1-x))- x - x^2/2 )/2. - Geoffrey Critzer, Nov 23 2012
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EXAMPLE
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a(4) = 9. There are 6 partitions of {1,2,3,4} into exactly three bocks and one way to put them in an undirected cycle of length three. There is one partition of {1,2,3,4} into four blocks and 3 ways to make an undirected cycle of length four. 6 + 3 = 9. - Geoffrey Critzer, Nov 23 2012
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MATHEMATICA
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a[n_] := Sum[ k!*StirlingS2[n-1, k], {k, 0, n-1}] - 2^(n-2); Table[a[n], {n, 3, 17}] (* From Jean-François Alcover, Nov 18 2011, after Manfred Goebel *)
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CROSSREFS
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Sequence in context: A016130 A115202 A155592 * A133120 A194650 A048742
Adjacent sequences: A002048 A002049 A002050 * A002052 A002053 A002054
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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