A246661 Run Length Transform of swinging factorials (A056040).

1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 6, 1, 1, 1, 2, 1, 1, 2, 6, 2, 2, 2, 4, 6, 6, 6, 30, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 6, 2, 2, 2, 4, 2, 2, 4, 12, 6, 6, 6, 12, 6, 6, 30, 20, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 6, 6, 1, 1, 1, 2, 1, 1

Offset: 0

Author

Peter Luschny, Sep 07 2014

Keywords

• nonn
• base

Comments

For the definition of the Run Length Transform see A246595.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A227349, A246588, A246595, A246596, A246660.

Programs

Mathematica

f[n_] := n!/Quotient[n, 2]!^2; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 85}] (* Jean-François Alcover, Jul 11 2017 *)

Python

# use RLT function from A278159
from math import factorial
def A246661(n): return RLT(n,lambda m: factorial(m)//factorial(m//2)**2) # Chai Wah Wu, Feb 04 2022

Sage

# uses[RLT from A246660]
A246661_list = lambda len: RLT(lambda n: factorial(n)/factorial(n//2)^2, len)
A246661_list(88)

Formula

a(2^n-1) = n$ where n$ is the swinging factorial of n, A056040(n).