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A139329
a(n) = (factorial of the number of 0's in the binary expansion of n).
3
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
0,5
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.
FORMULA
a(n) = A000142(A023416(n)) = A000142(A080791(n)). - Antti Karttunen, Oct 24 2017
MATHEMATICA
a[n_] := DigitCount[n, 2, 0]!; Array[a, 100, 0] (* Amiram Eldar, Jul 29 2023 *)
PROG
(PARI) a(n) = (#binary(n)-hammingweight(n))!; \\ Michel Marcus, Oct 24 2017
CROSSREFS
Cf. A000142, A023416, A080791, A093659 (factorial of the number of 1's in binary expansion of n).
Sequence in context: A294875 A293902 A300830 * A335432 A229557 A332700
KEYWORD
base,easy,nonn
AUTHOR
Max Sills, Apr 13 2008
EXTENSIONS
Locations of the name and the formula changed, more terms from Antti Karttunen, Oct 24 2017
STATUS
approved