A136494 Number of permutation symmetries in the binary expansion of n.

1, 1, 1, 2, 2, 2, 2, 6, 6, 4, 4, 6, 4, 6, 6, 24, 24, 12, 12, 12, 12, 12, 12, 24, 12, 12, 12, 24, 12, 24, 24, 120, 120, 48, 48, 36, 48, 36, 36, 48, 48, 36, 36, 48, 36, 48, 48, 120, 48, 36, 36, 48, 36, 48, 48, 120, 36, 48, 48, 120, 48, 120, 120, 720, 720

Offset: 0

Author

Max Sills, Apr 13 2008

Keywords

• base
• nonn

Examples

			a(14) = 6 because there are 3! permutation symmetries of 1's * the 0! permutation symmetries of 0's.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1023

Crossrefs

Cf. A000120, A080791, A093659, A139329.

Programs

Mathematica

a[n_] := Times @@ (DigitCount[n, 2]!); Array[a, 65, 0] (* Amiram Eldar, Jul 29 2023 *)

PARI

a(n) = {if(n==0, 1, my(w=hammingweight(n)); w!*(1+logint(n,2)-w)!)} \\ Andrew Howroyd, Jan 12 2020

Formula

a(n) = A093659(n) * A139329(n).

a(n) = A000120(n)! * A080791(n)!.

Extensions

Terms a(32) and beyond from Andrew Howroyd, Jan 12 2020