

A072187


Number of updown involutions of length n.


2



1, 1, 1, 1, 2, 3, 6, 11, 24, 51, 120, 283, 716, 1833, 4948, 13561, 38788, 112745, 339676, 1039929, 3283876, 10532747, 34717276, 116158851, 398257012, 1385117947, 4925094508, 17752742867, 65297807204, 243319812785, 923739847132, 3550638576721, 13885783706324
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OFFSET

0,5


COMMENTS



LINKS



FORMULA

G.f.: Sum_{n>=0} a(2n+1)x^(2n+1) = Sum_{i,j >= 0) arctan(x)^(2i+1) (log((1+x^2)/(1x^2)))^j E(2i+2j+1)/((2i+1)!j!4^j), where E(2i+2j+1) is an Euler number (A000111). There is a similar but more complicated generating function for a(2n).  Richard Stanley, Jan 02 2006


EXAMPLE

a(3)=1 since among the four involutions of length 3 (123, 213, 321, 132), only one is updown (132).


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



