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

Author

Paul D. Hanna, Dec 02 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000984, A135758.

Programs

Magma

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

Maple

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

Mathematica

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)

Formula

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