A139329 - OEIS

%I #26 Jul 29 2023 03:14:52

%S 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,

%T 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,

%U 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

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

%C 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.

%H Antti Karttunen, <a href="/A139329/b139329.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.

%F a(n) = A000142(A023416(n)) = A000142(A080791(n)). - _Antti Karttunen_, Oct 24 2017

%t a[n_] := DigitCount[n, 2, 0]!; Array[a, 100, 0] (* _Amiram Eldar_, Jul 29 2023 *)

%o (PARI) a(n) = (#binary(n)-hammingweight(n))!; \\ _Michel Marcus_, Oct 24 2017

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

%K base,easy,nonn

%O 0,5

%A _Max Sills_, Apr 13 2008

%E Locations of the name and the formula changed, more terms from _Antti Karttunen_, Oct 24 2017