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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.
2
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
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
Equals A000245(n) squared for n >= 1.
Sequence in context: A344298 A144821 A344253 * A199689 A181581 A137062
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 30 2020
STATUS
approved