OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1208
FORMULA
a(n) = A008302(2n,n).
a(n) ~ c * 3^(3*n - 1/2) / (sqrt(Pi*n) * 2^(2*n)), where c = QPochhammer(1/3) = A100220 = 0.5601260779279489449697922433141400143797363337983... - Vaclav Kotesovec, Jun 09 2025
EXAMPLE
a(0) = 1: the empty permutation.
a(1) = 1: 21.
a(2) = 5: 1342, 1423, 2143, 2314, 3124.
a(3) = 29: 123654, 124563, 124635, 125364, 125436, 126345, 132564, 132645, 134265, 134526, 135246, 142365, 142536, 143256, 152346, 213564, 213645, 214365, 214536, 215346, 231465, 231546, 234156, 241356, 312465, 312546, 314256, 321456, 412356.
MAPLE
a:= n-> coeff(series(mul((1-q^j)/(1-q), j=1..2*n), q, n+1), q, n):
seq(a(n), n=0..23);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 27 2025
STATUS
approved