A327493 a(n) = 2^A327492(n).

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

Author

Peter Luschny, Sep 27 2019

Keywords

• nonn

Crossrefs

Cf. A327492, A327491, A327494, A327495, A056040.

Programs

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

Maple

A327493 := n -> 2^(A327492_list(n+1)[n+1]):
seq(A327493(n), n = 0..26);

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

Formula

a(n) = denominator(b(n)) where b(n) = n!/(2^n*floor(n/2)!)^2 is the normalized swinging factorial (A056040).