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, 6892620648003551071800

Offset

0,2

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).

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

a(n) ~ 2^(4*n-1/2) / sqrt(Pi*n). - Amiram Eldar, Oct 16 2025

Mathematica

a[n_] := Binomial[4*n, 2*n] - 4*n * Binomial[2*n-2, n-1]; Array[a, 20, 0] (* Amiram Eldar, Oct 16 2025 *)

Prog

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

Crossrefs

Cf. A000984, A108558.

Sequence in context: A055024 A057411 A157058 * A357421 A071798 A338514

Adjacent sequences: A305690 A305691 A305692 * A305694 A305695 A305696

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 08 2018

Status

approved