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A136494
Number of permutation symmetries in the binary expansion of n.
1
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
0,4
LINKS
FORMULA
a(n) = A093659(n) * A139329(n).
a(n) = A000120(n)! * A080791(n)!.
EXAMPLE
a(14) = 6 because there are 3! permutation symmetries of 1's * the 0! permutation symmetries of 0's.
MATHEMATICA
a[n_] := Times @@ (DigitCount[n, 2]!); Array[a, 65, 0] (* Amiram Eldar, Jul 29 2023 *)
PROG
(PARI) a(n) = {if(n==0, 1, my(w=hammingweight(n)); w!*(1+logint(n, 2)-w)!)} \\ Andrew Howroyd, Jan 12 2020
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Max Sills, Apr 13 2008
EXTENSIONS
Terms a(32) and beyond from Andrew Howroyd, Jan 12 2020
STATUS
approved