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a(n) = binomial(4*n, 2*n) - 4*n*binomial(2*n-2, n-1).
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%I #17 Jun 08 2018 13:51:07

%S 1,2,54,852,12550,183356,2698108,40090728,600970566,9074671980,

%T 137844584020,2104090834456,32247569822364,495918392331992,

%U 7648690018326840,118264579157865424,1832624131015069254,28453041434367110220,442512540108817131364

%N a(n) = binomial(4*n, 2*n) - 4*n*binomial(2*n-2, n-1).

%H Seiichi Manyama, <a href="/A305693/b305693.txt">Table of n, a(n) for n = 0..500</a>

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1098/rspa.1997.0126">Low-Dimensional Lattices VII: Coordination Sequences</a>, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%F a(n) = A000984(2*n) - 4*n*A000984(n-1) for n > 0.

%F G.f.: sqrt(1 + sqrt(1 - 16*x))/sqrt(2*(1 - 16*x)) - 4*x*(1 - 2*x)/(1 - 4*x)^(3/2). - _Ilya Gutkovskiy_, Jun 08 2018

%o (PARI) {a(n) = binomial(4*n, 2*n)-4*n*binomial(2*n-2, n-1)}

%Y Cf. A000984, A108558.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 08 2018