A249395 Number of generalized cycle-up-down permutations of [n].

1, 1, 2, 6, 21, 97, 491, 2989, 19756, 148444, 1205731, 10767889, 103379533, 1069512329, 11819221164, 138980503372, 1734555299547, 22842846011691, 317403042567207, 4626310914540965, 70776622667767954, 1130784058442869122, 18877678724072172281

Offset

0,3

Links

Table of n, a(n) for n=0..22.

E. Deutsch, S. Elizalde, Cycle up-down permutations, arXiv:0909.5199

Formula

E.g.f.: sec(x)*exp[sec x- 1+(1-x/2)*tan x].

Maple

sec(x)*exp(sec(x)-1+(1-x/2)*tan(x)) :
taylor(%, x=0, 30) :
gfun[seriestolist](%) :
seq(op(i, %)*(i-1)!, i=1..nops(%)) ;

Crossrefs

Sequence in context: A183950 A001928 A005638 * A008988 A061232 A020091

Adjacent sequences: A249392 A249393 A249394 * A249396 A249397 A249398

Keyword

nonn,easy

Author

R. J. Mathar, Oct 27 2014

Status

approved