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A005388
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Number of degree-n permutations of order a power of 2.
(Formerly M1293)
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13
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1, 1, 2, 4, 16, 56, 256, 1072, 11264, 78976, 672256, 4653056, 49810432, 433429504, 4448608256, 39221579776, 1914926104576, 29475151020032, 501759779405824, 6238907914387456, 120652091860975616, 1751735807564578816, 29062253310781161472, 398033706586943258624
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OFFSET
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0,3
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COMMENTS
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Differs from A053503 first at n=32. - Alois P. Heinz, Feb 14 2013
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
J. M. Møller, Euler characteristics of equivariant subcategories, arXiv preprint arXiv:1502.01317, 2015. See page 20.
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.
A. Recski, Enumerating partitional matroids, Preprint.
A. Recski & N. J. A. Sloane, Correspondence, 1975
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FORMULA
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E.g.f.: exp(Sum(x^(2^m)/2^m, m >=0)).
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MAPLE
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a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(mul(n-i, i=1..2^j-1)*a(n-2^j), j=0..ilog2(n))))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Feb 14 2013
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MATHEMATICA
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max = 23; CoefficientList[ Series[ Exp[ Sum[x^2^m/2^m, {m, 0, max}]], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Sep 10 2013 *)
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CROSSREFS
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Cf. A000085, A001470, A001472, A053495-A053505.
Cf. A053503.
Sequence in context: A001472 A053498 * A053503 A153957 A068789 A009624
Adjacent sequences: A005385 A005386 A005387 * A005389 A005390 A005391
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane and J. H. Conway
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STATUS
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approved
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