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 A000704 Number of degree-n even permutations of order dividing 2. (Formerly M3511 N1427) 15
 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 J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, Inc. New York, 1958 (Chap. 4, Problem 22). 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 Lev Glebsky, Melany Licón, Luis Manuel Rivera, On the number of even roots of permutations, arXiv:1907.00548 [math.CO], 2019. A. M. Goyt, Avoidance of partitions of a 3-element set, arXiv:math/0603481 [math.CO], 2006-2007. 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.: exp(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 a[n_] := Sum[(4i - 1)!! Binomial[n, 4i], {i, 0, n/4}]; Array[a, 30, 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 *) PROG (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x)*cosh(x^2/2) )) \\ G. C. Greubel, Jul 02 2019 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Cosh(x^2/2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 02 2019 (Sage) m = 30; T = taylor(exp(x)*cosh(x^2/2), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Jul 02 2019 CROSSREFS Sequence in context: A213480 A306302 A159940 * A007315 A055342 A213292 Adjacent sequences:  A000701 A000702 A000703 * A000705 A000706 A000707 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Harvey P. Dale, Nov 29 2013 STATUS approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)