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

0,4

Comments

For the definition of the Run Length Transform see A246595.

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A025242 A356696 A163982 * A246660 A346422 A245405

Adjacent sequences: A246658 A246659 A246660 * A246662 A246663 A246664

Keyword

nonn,base

Author

Peter Luschny, Sep 07 2014

Status

approved