OFFSET
0,3
LINKS
Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.18 at page 10.
FORMULA
a(n) = A000035(n) + 2^n*Sum_{i=0..floor((n-2)/2)} binomial(2*(n - i)- 3, n - 1).
a(n) ~ 8^(n-1)*hypergeom([1, 1 - n/2, (3 - n)/2], [(3 - 2*n)/2, 2 - n], 1)/sqrt(n*Pi).
MATHEMATICA
a[n_] := (1-(-1)^n)/2 + 2^n*Sum[Binomial[2(n-i)-3, n-1], {i, 0, Floor[(n-2)/2]}]; Array[a, 24, 0]
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jan 20 2024
STATUS
approved