A139329 -id:A139329 - cp's OEIS frontend

A093659 First column of lower triangular matrix A093658; factorial of the number of 1's in binary expansion of n.

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

Offset: 0

Paul D. Hanna, Apr 08 2004

a(n) is the number of compositions of n into distinct powers of 2. - Vladimir Shevelev, Jan 15 2014

Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

Cf. A000079, A000523, A023359, A093658, A093677, A000120, A000142, A139329.

a:= n-> add(i,i=Bits[Split](n))!:
seq(a(n), n=0..80);  # Alois P. Heinz, Nov 02 2024

Table[DigitCount[n,2,1]!,{n,0,70}] (* Harvey P. Dale, Jul 09 2019 *)

from math import factorial
def a(n): return factorial(n.bit_count()) # Michael S. Branicky, Nov 02 2024

a(2^n) = n! for n>=0. a(2^n+2^m) = a(2^(m+1)) for n>m>=0.

a(n) = A000120(n)! = A000142(A000120(n)).

A136494 Number of permutation symmetries in the binary expansion of n.

Original entry on oeis.org

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

Max Sills, Apr 13 2008

			a(14) = 6 because there are 3! permutation symmetries of 1's * the 0! permutation symmetries of 0's.

Andrew Howroyd, Table of n, a(n) for n = 0..1023

Cf. A000120, A080791, A093659, A139329.

a[n_] := Times @@ (DigitCount[n, 2]!); Array[a, 65, 0] (* Amiram Eldar, Jul 29 2023 *)

a(n) = {if(n==0, 1, my(w=hammingweight(n)); w!*(1+logint(n,2)-w)!)} \\ Andrew Howroyd, Jan 12 2020

a(n) = A093659(n) * A139329(n).

a(n) = A000120(n)! * A080791(n)!.

Terms a(32) and beyond from Andrew Howroyd, Jan 12 2020

cp's OEIS Frontend

A093659 First column of lower triangular matrix A093658; factorial of the number of 1's in binary expansion of n.

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