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A000704 Number of degree-n even permutations of order dividing 2.
(Formerly M3511 N1427)
13
1, 1, 1, 1, 4, 16, 46, 106, 316, 1324, 5356, 18316, 63856, 272416, 1264264, 5409496, 22302736, 101343376, 507711376, 2495918224, 11798364736, 58074029056, 309240315616, 1670570920096, 8792390355904, 46886941456576, 264381946998976, 1533013006902976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of odd partitions of an n-element set avoiding the pattern 123 (see Goyt paper). - Ralf Stephan, May 08 2007

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

A. M. Goyt, Avoidance of partitions of a 3-element set

L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

FORMULA

E.g.f.: e^x cosh ( x^2 / 2 ).

a(n) = sum[i = 0, floor(n/4), C(n, 4i)*(4i-1)!! ]. - Ralf Stephan, May 08 2007 [Corrected by Sean A. Irvine, Mar 01 2011]

Conjecture: a(n) -3*a(n-1) +3*a(n-2) -a(n-3) -(n-1)*(n-3)*a(n-4) +(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Jun 03 2014

MATHEMATICA

f[n_] := Sum[(4i - 1)!! Binomial[n, 4i], {i, 0, n/4}]; Array[f, 22, 0] (* Robert G. Wilson v *)

With[{nn = 30}, CoefficientList[Series[Exp[x]Cosh[x^2/2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 29 2013 *)

CROSSREFS

Sequence in context: A097125 A213480 A159940 * A007315 A055342 A213292

Adjacent sequences:  A000701 A000702 A000703 * A000705 A000706 A000707

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and J. H. Conway

EXTENSIONS

More terms from Harvey P. Dale, Nov 29 2013

STATUS

approved

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Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)