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a(n) = 2^(n - HammingWeight(n)) * binomial(2*n, n).
1

%I #8 Mar 31 2024 15:19:13

%S 1,2,12,40,560,2016,14784,54912,1647360,6223360,47297536,180590592,

%T 2769055744,10650214400,82158796800,317680680960,19696202219520,

%U 76467608616960,594748067020800,2316387208396800,36135640450990080,141101072237199360,1103153837490831360

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

%H Paolo Xausa, <a href="/A371357/b371357.txt">Table of n, a(n) for n = 0..1000</a>

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

%p HammingWeight := n -> add(convert(n, base, 2)):

%p a := n -> 2^(n - HammingWeight(n))*binomial(2*n, n):

%p seq(a(n), n = 0..22);

%t Array[2^(# - DigitCount[#, 2, 1]) * Binomial[2*#, #] &, 25, 0] (* _Paolo Xausa_, Mar 31 2024 *)

%Y Cf. A060818, A000984.

%K nonn

%O 0,2

%A _Peter Luschny_, Mar 23 2024