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

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

Offset

0,4

Links

Table of n, a(n) for n=0..12.

Index entries for sequences related to factorial numbers

Formula

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

Example

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

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 *)

Prog

(Python)
from gmpy2 import fac, popcount
def A348651(n): return popcount(fac(fac(n))) # Chai Wah Wu, Oct 28 2021
(PARI) a(n) = hammingweight((n!)!); \\ Michel Marcus, Oct 29 2021

Crossrefs

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

Sequence in context: A302609 A181197 A217807 * A360584 A127770 A121630

Adjacent sequences: A348648 A348649 A348650 * A348652 A348653 A348654

Keyword

nonn,base,more

Author

Alois P. Heinz, Oct 27 2021

Extensions

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

Status

approved