A338727 a(n) = C(n+1)^2 - 2*C(n+1)*C(n) + C(n)^2, where C() is a Catalan number; a(0) = 1.

1, 1, 9, 81, 784, 8100, 88209, 1002001, 11778624, 142420356, 1763160100, 22268399076, 286105172544, 3730846771600, 49286086364025, 658580586980625, 8890060997894400, 121099761397088100, 1663131325207760100, 23009839285003272900, 320486852887891560000, 4491184012659823424400, 63291012091734041000100

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = A000245(n)^2 for n >= 1.

D-finite with recurrence (n+2)^2*(n-1)^2*a(n) - 4*n^2*(2*n-1)^2*a(n-1) = 0. - R. J. Mathar, Dec 11 2020

a(n) = A213600(2n,2) for n >= 1. - Alois P. Heinz, Oct 07 2022

a(n) ~ 9 * 16^n / (n^3 * Pi). - Amiram Eldar, Oct 11 2025

Maple

A338727 := proc(n)
    if n = 0 then
        1;
    else
        (A000108(n+1)-A000108(n))^2 ;
    end if;
end proc:
seq( A338727(n), n=0..30) ; # R. J. Mathar, Dec 11 2020

Mathematica

With[{c = CatalanNumber}, a[n_] := (c[n+1] - c[n])^2; a[0] = 1; Array[a, 25, 0]] (* Amiram Eldar, Oct 11 2025 *)

Crossrefs

Cf. A000108, A000245, A005700, A213600.

Sequence in context: A344298 A144821 A344253 * A199689 A181581 A137062

Adjacent sequences: A338724 A338725 A338726 * A338728 A338729 A338730

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 30 2020

Status

approved