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A115455 a(n) = number of reverse alternating fixed-point-free involutions w on 1,2,...,2n, i.e., w(1) < w(2) > w(3) < w(4) > ... < w(2n), w^2=1 and w(i) != i for all i. 2
1, 0, 1, 1, 4, 13, 59, 308, 1871, 12879, 99144, 843735, 7865177, 79698760, 872235089, 10253148625, 128839087676, 1723418002261, 24450430660739, 366702601116524, 5796979684239647, 96339860422218143, 1679159568980521104, 30628034488033962287 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

R. P. Stanley, Permutations, Joint Mathematics Meeting, 2009.

R. P. Stanley, Alternating permutations and symmetric functions, J. Comb. Theory A 114 (3) (2007) 436-460

FORMULA

G.f.: (1-x^2)^{-1/4} (1+x)^{-1/2} Sum_{k>=0} E_{2k} v^k/k!, where E_{2k} is an Euler number and v = (1/4)*log((1+x)/(1-x)).

EXAMPLE

a(3)=1 because there is one reverse alternating fixed-point-free involution on 1,...,6, viz., 351624.

MATHEMATICA

Table[SeriesCoefficient[(1-x^2)^(-1/4)*(1+x)^(-1/2)*Sum[(-1)^k*EulerE[2*k]*(1/4*Log[(1+x)/(1-x)])^k/k!, {k, 0, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 29 2014 *)

CROSSREFS

Cf. A000085, A000111, A001147, A007779.

Sequence in context: A026663 A149486 A317891 * A241470 A219367 A149487

Adjacent sequences:  A115452 A115453 A115454 * A115456 A115457 A115458

KEYWORD

easy,nonn

AUTHOR

Richard Stanley, Jan 22 2006

STATUS

approved

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Last modified May 15 17:50 EDT 2021. Contains 343920 sequences. (Running on oeis4.)