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A005388 Number of degree-n permutations of order a power of 2.
(Formerly M1293)
15
1, 1, 2, 4, 16, 56, 256, 1072, 11264, 78976, 672256, 4653056, 49810432, 433429504, 4448608256, 39221579776, 1914926104576, 29475151020032, 501759779405824, 6238907914387456, 120652091860975616, 1751735807564578816, 29062253310781161472, 398033706586943258624 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Differs from A053503 first at n=32. - Alois P. Heinz, Feb 14 2013
REFERENCES
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.
LINKS
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
FORMULA
E.g.f.: exp(Sum(x^(2^m)/2^m, m >=0)).
MAPLE
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
MATHEMATICA
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 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
f:= func< x | Exp( (&+[x^(2^j)/2^j: j in [0..14]]) ) >;
Coefficients(R!(Laplace( f(x) ))); // G. C. Greubel, Nov 17 2022
(SageMath)
def f(x): return exp(sum(x^(2^j)/2^j for j in range(15)))
def A005388_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).egf_to_ogf().list()
A005388_list(40) # G. C. Greubel, Nov 17 2022
CROSSREFS
Sequence in context: A306519 A001472 A053498 * A053503 A308381 A153957
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)