A371357 a(n) = 2^(n - HammingWeight(n)) * binomial(2*n, n).

1, 2, 12, 40, 560, 2016, 14784, 54912, 1647360, 6223360, 47297536, 180590592, 2769055744, 10650214400, 82158796800, 317680680960, 19696202219520, 76467608616960, 594748067020800, 2316387208396800, 36135640450990080, 141101072237199360, 1103153837490831360

Offset: 0

Author

Peter Luschny, Mar 23 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A060818, A000984.

Programs

Maple

HammingWeight := n -> add(convert(n, base, 2)):
a := n -> 2^(n - HammingWeight(n))*binomial(2*n, n):
seq(a(n), n = 0..22);

Mathematica

Array[2^(# - DigitCount[#, 2, 1]) * Binomial[2*#, #] &, 25, 0] (* Paolo Xausa, Mar 31 2024 *)

Formula

a(n) = A060818(n) * A000984(n).