A348651 Number of ones in the binary expansion of (n!)!.

1, 1, 1, 4, 29, 293, 2566, 24844, 259437, 2908263, 35102629, 455204360, 6321171774

Offset: 0

Author

Alois P. Heinz, Oct 27 2021

Keywords

• nonn
• base
• more

Examples

			a(3) = 4 because (3!)! = 6! = 720 = 1011010000_2 which has 4 ones.
		

Links

• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000120, A000142, A000197, A079584, A152168, A301861.

Programs

Maple

a:= n-> add(i, i=Bits[Split](n!!)):
seq(a(n), n=0..10);

Mathematica

a[n_] := DigitCount[(n!)!, 2, 1]; Array[a, 10, 0] (* Amiram Eldar, Oct 29 2021 *)

PARI

a(n) = hammingweight((n!)!); \\ Michel Marcus, Oct 29 2021

Python

from gmpy2 import fac, popcount
def A348651(n): return popcount(fac(fac(n))) # Chai Wah Wu, Oct 28 2021

Formula

a(n) = A000120(A000197(n)).

Extensions

a(11)-a(12) from Chai Wah Wu, Oct 28 2021