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

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

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

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

Crossrefs

Cf. A000108, A005700, A213600.

Equals A000245(n) squared for n >= 1.

Sequence in context: A344298 A144821 A344253 * A199689 A181581 A137062

Adjacent sequences: A338724 A338725 A338726 * A338728 A338729 A338730

Keyword

nonn

Author

N. J. A. Sloane, Nov 30 2020

Status

approved