A305693 a(n) = binomial(4*n, 2*n) - 4*n*binomial(2*n-2, n-1).

1, 2, 54, 852, 12550, 183356, 2698108, 40090728, 600970566, 9074671980, 137844584020, 2104090834456, 32247569822364, 495918392331992, 7648690018326840, 118264579157865424, 1832624131015069254, 28453041434367110220, 442512540108817131364

Offset: 0

Author

Seiichi Manyama, Jun 08 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Crossrefs

Cf. A000984, A108558.

Programs

PARI

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

Formula

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

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