This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139329 #26 Jul 29 2023 03:14:52 %S A139329 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 A139329 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 A139329 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 A139329 a(n) = (factorial of the number of 0's in the binary expansion of n). %C A139329 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 A139329 Antti Karttunen, <a href="/A139329/b139329.txt">Table of n, a(n) for n = 0..8191</a> %H A139329 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>. %F A139329 a(n) = A000142(A023416(n)) = A000142(A080791(n)). - _Antti Karttunen_, Oct 24 2017 %t A139329 a[n_] := DigitCount[n, 2, 0]!; Array[a, 100, 0] (* _Amiram Eldar_, Jul 29 2023 *) %o A139329 (PARI) a(n) = (#binary(n)-hammingweight(n))!; \\ _Michel Marcus_, Oct 24 2017 %Y A139329 Cf. A000142, A023416, A080791, A093659 (factorial of the number of 1's in binary expansion of n). %K A139329 base,easy,nonn %O A139329 0,5 %A A139329 _Max Sills_, Apr 13 2008 %E A139329 Locations of the name and the formula changed, more terms from _Antti Karttunen_, Oct 24 2017