A093659 - OEIS

%I #28 Nov 02 2024 12:56:12

%S 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,

%T 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,

%U 24,120,24,120,120,720,1,2,2,6,2,6,6,24,2,6,6,24,6

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

%C a(n) is the number of compositions of n into distinct powers of 2. - _Vladimir Shevelev_, Jan 15 2014

%H Antti Karttunen, <a href="/A093659/b093659.txt">Table of n, a(n) for n = 0..8192</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

%p a:= n-> add(i,i=Bits[Split](n))!:

%p seq(a(n), n=0..80);  # _Alois P. Heinz_, Nov 02 2024

%t Table[DigitCount[n,2,1]!,{n,0,70}] (* _Harvey P. Dale_, Jul 09 2019 *)

%o (Python)

%o from math import factorial

%o def a(n): return factorial(n.bit_count()) # _Michael S. Branicky_, Nov 02 2024

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

%K nonn,base

%O 0,4

%A _Paul D. Hanna_, Apr 08 2004