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

Author

Paul D. Hanna, Apr 08 2004

Keywords

• nonn
• base

Comments

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

Python

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

Formula

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)).