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 A005981 Number of 2 up, 2 down, 2 up, ... permutations of length 2n + 1. (Formerly M4276) 9
 1, 1, 6, 71, 1456, 45541, 2020656, 120686411, 9336345856, 908138776681, 108480272749056, 15611712012050351, 2664103110372192256, 531909061958526321421, 122840808510269863827456, 32491881630252866646683891, 9758611490955498257378246656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). P. R. Stein, personal communication. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 Nicolas Basset, Counting and generating permutations using timed languages, 2013. Nicolas Basset, Counting and generating permutations in regular classes of permutations, HAL Id: hal-01093994, 2014. B. Shapiro and A. Vainshtein, Counting real rational functions with all real critical values, Moscow Math. J., 3 (2003), 647-659. P. R. Stein & N. J. A. Sloane, Correspondence, 1975 Eric Weisstein's World of Mathematics, Generalized Hyperbolic Functions FORMULA E.g.f.: x + Sum_{n>=1} a(n)*(x^(2n+1))/(2n+1)! = (f(0,x)*f(1,x) -f(2,x)*f(3,x)+ f(3,x))/(f(0,x)^2 - f(1,x)*f(3,x)), where f(j,x) = Sum_{k>=0} (x^(4k+j))/(4k+j)!, j = 0,1,2,3, is the j-th generalized hyperbolic function. - Peter Bala, Jul 13 2007 Basset (2013) gives an e.g.f. involving trigonometric and hyperbolic functions. - N. J. A. Sloane, Dec 24 2013 a(n) ~ 4 * (2*n+1)! / (tan(r/2)^2 * r^(2*n+2)), where r = A076417 = 1.8751040687119611664453082410782141625701117335310699882454137131... is the root of the equation cos(r)*cosh(r) = -1. - Vaclav Kotesovec, Feb 01 2015 MAPLE g:=((cosh(x)-1)*sin(x)+(cos(x)+1)*sinh(x))/(cos(x)*cosh(x)+1): series(%, x, 35): seq(n!*coeff(%, x, n), n=1..34, 2); # Peter Luschny, Feb 07 2017 MATHEMATICA egf = ((Cosh[x]-1)*Sin[x]+(Cos[x]+1)*Sinh[x])/(Cos[x]*Cosh[x]+1); a[n_] := SeriesCoefficient[egf, {x, 0, 2*n+1}]*(2*n+1)!; Array[a, 17, 0] (* Jean-François Alcover, Mar 13 2014 *) CROSSREFS Bisection of A058258. Cf. A131453, A131454, A131455, A076417. Sequence in context: A218676 A127135 A187651 * A024272 A167813 A242232 Adjacent sequences:  A005978 A005979 A005980 * A005982 A005983 A005984 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)