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
Examples
a(3) = 4 because (3!)! = 6! = 720 = 1011010000_2 which has 4 ones.
Programs
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Maple
a:= n-> add(i, i=Bits[Split](n!!)): seq(a(n), n=0..10);
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Mathematica
a[n_] := DigitCount[(n!)!, 2, 1]; Array[a, 10, 0] (* Amiram Eldar, Oct 29 2021 *)
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PARI
a(n) = hammingweight((n!)!); \\ Michel Marcus, Oct 29 2021
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Python
from gmpy2 import fac, popcount def A348651(n): return popcount(fac(fac(n))) # Chai Wah Wu, Oct 28 2021
Extensions
a(11)-a(12) from Chai Wah Wu, Oct 28 2021