A139329 a(n) = (factorial of the number of 0's in the binary expansion of n).

1, 1, 1, 1, 2, 1, 1, 1, 6, 2, 2, 1, 2, 1, 1, 1, 24, 6, 6, 2, 6, 2, 2, 1, 6, 2, 2, 1, 2, 1, 1, 1, 120, 24, 24, 6, 24, 6, 6, 2, 24, 6, 6, 2, 6, 2, 2, 1, 24, 6, 6, 2, 6, 2, 2, 1, 6, 2, 2, 1, 2, 1, 1, 1, 720, 120, 120, 24, 120, 24, 24, 6, 120, 24, 24, 6, 24, 6, 6, 2, 120, 24, 24, 6, 24, 6, 6, 2, 24, 6, 6, 2, 6, 2, 2, 1, 120

Offset: 0

Author

Max Sills, Apr 13 2008

Keywords

• base
• easy
• nonn

Comments

Number of permutation symmetries of the 0's in the binary expansion of n. Consider the symmetric group that permutes floor(log_2(n)) elements acting on the 0's.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000142, A023416, A080791, A093659 (factorial of the number of 1's in binary expansion of n).

Programs

Mathematica

a[n_] := DigitCount[n, 2, 0]!; Array[a, 100, 0] (* Amiram Eldar, Jul 29 2023 *)

PARI

a(n) = (#binary(n)-hammingweight(n))!; \\ Michel Marcus, Oct 24 2017

Formula

a(n) = A000142(A023416(n)) = A000142(A080791(n)). - Antti Karttunen, Oct 24 2017

Extensions

Locations of the name and the formula changed, more terms from Antti Karttunen, Oct 24 2017