A135758 -id:A135758 - cp's OEIS frontend

A135757 Central binomial coefficients at triangular positions: a(n) = A000984(n(n+1)/2).

1, 2, 20, 924, 184756, 155117520, 538257874440, 7648690600760440, 442512540276836779204, 103827421287553411369671120, 98527218530093856775578873054432, 377389666165540953244592352291892721700, 5825874245311064218315521996517139009907512400

Offset: 0

Paul D. Hanna, Dec 02 2007

G. C. Greubel, Table of n, a(n) for n = 0..50

Cf. A000984, A135758.

[Binomial(n*(n+1), n*(n+1) div 2): n in [0..15]]; // Vincenzo Librandi, Nov 08 2016

seq(binomial(n*(n+1),n*(n+1)/2),n=0..20); # Robert Israel, Nov 08 2016

Table[Binomial[n*(n + 1), n*(n + 1)/2], {n,0,10}] (* G. C. Greubel, Nov 07 2016 *)

PARI
```
a(n)=binomial(n*(n+1),n*(n+1)/2)
```

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

a(n) ~ 2^(n^2+n) sqrt(2/Pi) (1/n - 1/(2n^2) + 1/(8n^3) + ...). - Robert Israel, Nov 08 2016

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

Original entry on oeis.org

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

Offset: 0

Paul D. Hanna, Jul 17 2012

nonn

Cf. A135758, A201555.

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

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

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

cp's OEIS Frontend

A135757 Central binomial coefficients at triangular positions: a(n) = A000984(n(n+1)/2).

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