OFFSET
0,4
COMMENTS
a(n) is also the number of n-permutations with exactly one square root. Cf. A003483 which counts n-permutations with at least one square root.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (1 + x)*((1+x)/(1-x))^(1/2)*exp(-x).
a(n) ~ 4*n^n/exp(n+1). - Vaclav Kotesovec, Oct 08 2013
EXAMPLE
a(6)= 184 because we have 144 6-permutations of the type (1,2,3,4,5)(6) and 40 of the type (1,2,3)(4,5,6). These have exactly one square root: (1,4,2,5,3)(6) and (1,3,2)(4,6,5).
MATHEMATICA
nn=22; Range[0, nn]! CoefficientList[Series[(1+x)((1+x)/(1-x))^(1/2) Exp[-x], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Mar 08 2013
STATUS
approved