OFFSET
0,3
COMMENTS
All terms are odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..448
Wikipedia, Permutation
FORMULA
a(n) = A084938(2n,n).
a(n) = [x^n] (1/(1 - x/(1 - x/(1 - 2*x/(1 - 2*x/(1 - 3*x/(1 - 3*x/(1 - ...))))))))^n, a continued fraction. - Ilya Gutkovskiy, Sep 29 2017
a(n) ~ exp(1) * n * n!. - Vaclav Kotesovec, Sep 29 2017
EXAMPLE
a(2) = 5: (1)(2,3,4), (1)(2,4,3), (1,2)(3,4), (1,2,3)(4), (1,3,2)(4).
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, n!,
add(b(n-j, i-1)*j!, j=0..n))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25);
MATHEMATICA
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2]*x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 29 2017 *)
Table[SeriesCoefficient[Sum[k!*x^k, {k, 0, n}]^n, {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Aug 10 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 02 2017
STATUS
approved