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

Author

N. J. A. Sloane, Nov 30 2020

Keywords

• nonn

Crossrefs

Cf. A000108, A005700, A213600.

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

Programs

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

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