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Catalan numbers at square positions: a(n) = A000108(n^2).
2

%I #5 May 27 2013 08:54:06

%S 1,1,14,4862,35357670,4861946401452,11959798385860453492,

%T 509552245179617138054608572,368479169875816659479009042713546950,

%U 4462290049988320482463241297506133183499654740,896519947090131496687170070074100632420837521538745909320

%N Catalan numbers at square positions: a(n) = A000108(n^2).

%F a(n) = binomial(2*n^2, n^2) / (n^2 + 1).

%t CatalanNumber[Range[0,10]^2] (* _Harvey P. Dale_, May 27 2013 *)

%o (PARI) {a(n)=binomial(2*n^2,n^2)/(n^2+1)}

%o for(n=0,15,print1(a(n),", "))

%Y Cf. A135758, A201555.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 17 2012