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A024255 a(0)=0, a(n) = n*E(2n-1) for n >= 1, where E(n) = A000111(n) are the Euler (or up-down) numbers. 3
0, 1, 4, 48, 1088, 39680, 2122752, 156577792, 15230058496, 1888788086784, 290888851128320, 54466478584365056, 12185086638082228224, 3209979242472703787008, 983522422455215438430208, 346787762817143967622103040, 139423404114002708738732982272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of cyclically alternating permutations of length 2n. Example: a(2)=4 because we have 1324, 1423, 2314, and 2413 (3412 is alternating but not cyclically alternating).

REFERENCES

G. Kreweras, Les préordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

N. D. Elkies, On the sums Sum((4k+1)^(-n),k,-inf,+inf), arXiv:math/0101168 [math.CA], 2001-2003.

N. D. Elkies, On the sums Sum_{k = -infinity .. infinity} (4k+1)^(-n), Amer. Math. Monthly, 110 (No. 7, 2003), 561-573.

FORMULA

a(n) = 2^(n-1)*(2^n-1)*|B_n|.

E.g.f.: tan(x)*x/2 (even part).

a(n) = (2*n)!*Pi^(-2*n)*(4^n-1)*Li{2*n}(1) for n > 0. - Peter Luschny, Jun 29 2012

G.f.: Q(0)*x/(1-4*x), where Q(k) = 1 - 16*x^2*(k+2)*(k+1)^3/( 16*x^2*(k+2)*(k+1)^3 - (1 - 8*x*k^2 - 12*x*k -4*x)*(1 - 8*x*k^2 - 28*x*k -24*x)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 23 2013

MAPLE

a := n -> (-1)^n*2^(2*n-1)*(1-2^(2*n))*bernoulli(2*n); # Peter Luschny, Jun 08 2009

MATHEMATICA

nn = 30; t = Range[0, nn]! CoefficientList[Series[Tan[x]*x/2, {x, 0, nn}], x]; Take[t, {1, nn, 2}]

CROSSREFS

Cf. A009752.

Sequence in context: A138448 A071221 A198038 * A211045 A296838 A211049

Adjacent sequences:  A024252 A024253 A024254 * A024256 A024257 A024258

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Edited by Emeric Deutsch, Jul 01 2009

STATUS

approved

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Last modified October 20 17:33 EDT 2018. Contains 316393 sequences. (Running on oeis4.)