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A327493
a(n) = 2^A327492(n).
6
1, 4, 8, 32, 128, 512, 1024, 4096, 32768, 131072, 262144, 1048576, 4194304, 16777216, 33554432, 134217728, 2147483648, 8589934592, 17179869184, 68719476736, 274877906944, 1099511627776, 2199023255552, 8796093022208, 70368744177664, 281474976710656, 562949953421312
OFFSET
0,2
FORMULA
a(n) = denominator(b(n)) where b(n) = n!/(2^n*floor(n/2)!)^2 is the normalized swinging factorial (A056040).
MAPLE
A327493 := n -> 2^(A327492_list(n+1)[n+1]):
seq(A327493(n), n = 0..26);
PROG
(PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, n, a[n+1] = a[n] * 2^if(n%4, n%2 + 1, valuation(n, 2))); a} \\ Andrew Howroyd, Sep 28 2019
(PARI) a(n)={ denominator(sum(j=0, n, j!/(2^j*(j\2)!)^2)) } \\ Andrew Howroyd, Sep 28 2019
(Julia)
bitcount(n) = sum(digits(n, base = 2))
A327493(n) = 2^(2n - bitcount(n) + mod(n, 2))
[A327493(n) for n in 0:26] |> println # Peter Luschny, Oct 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 27 2019
STATUS
approved