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

0,4

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

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)).

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 *)

Prog

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

Crossrefs

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

Sequence in context: A285003 A364872 A284002 * A306714 A200745 A067541

Adjacent sequences: A093656 A093657 A093658 * A093660 A093661 A093662

Keyword

nonn,base

Author

Paul D. Hanna, Apr 08 2004

Status

approved