A214441 Catalan numbers at square positions: a(n) = A000108(n^2).

1, 1, 14, 4862, 35357670, 4861946401452, 11959798385860453492, 509552245179617138054608572, 368479169875816659479009042713546950, 4462290049988320482463241297506133183499654740, 896519947090131496687170070074100632420837521538745909320

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Formula

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

a(n) ~ 4^(n^2) / (n^3 * sqrt(Pi)). - Amiram Eldar, Oct 09 2025

Mathematica

CatalanNumber[Range[0, 10]^2] (* Harvey P. Dale, May 27 2013 *)

Prog

(PARI) {a(n)=binomial(2*n^2, n^2)/(n^2+1)}
for(n=0, 15, print1(a(n), ", "))

Crossrefs

Cf. A000108, A135758, A201555.

Sequence in context: A188955 A157824 A180588 * A241326 A344689 A159372

Adjacent sequences: A214438 A214439 A214440 * A214442 A214443 A214444

Keyword

nonn,easy

Author

Paul D. Hanna, Jul 17 2012

Status

approved