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
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
FORMULA
E.g.f.: exp(Sum_{m>=0} x^(2^m)/2^m).
E.g.f.: 1/Product_{k>=1} (1 - x^(2*k-1))^(mu(2*k-1)/(2*k-1)), where mu() is the Moebius function. - Seiichi Manyama, Jul 06 2024
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
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved