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

%I A338727 #12 Jan 19 2024 06:01:33
%S A338727 1,1,9,81,784,8100,88209,1002001,11778624,142420356,1763160100,
%T A338727 22268399076,286105172544,3730846771600,49286086364025,
%U A338727 658580586980625,8890060997894400,121099761397088100,1663131325207760100,23009839285003272900,320486852887891560000,4491184012659823424400,63291012091734041000100
%N A338727 a(n) = C(n+1)^2 - 2*C(n+1)*C(n) + C(n)^2, where C() is a Catalan number.
%F A338727 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
%F A338727 a(n) = A213600(2n,2) for n>=1. - _Alois P. Heinz_, Oct 07 2022
%p A338727 A338727 := proc(n)
%p A338727     if n = 0 then
%p A338727         1;
%p A338727     else
%p A338727         (A000108(n+1)-A000108(n))^2 ;
%p A338727     end if;
%p A338727 end proc:
%p A338727 seq( A338727(n),n=0..30) ; # _R. J. Mathar_, Dec 11 2020
%Y A338727 Cf. A000108, A005700, A213600.
%Y A338727 Equals A000245(n) squared for n >= 1.
%K A338727 nonn
%O A338727 0,3
%A A338727 _N. J. A. Sloane_, Nov 30 2020