A070780 a(n) = binomial((n+1)^2,n).

1, 4, 36, 560, 12650, 376992, 13983816, 621216192, 32164253550, 1902231808400, 126524771308936, 9349109217266832, 759825846558448488, 67362990324409227840, 6469590128756692755600, 669128737063722082963200, 74148585178960981066746390, 8764445804610791475090220464, 1100718583140907766992803808200

Offset: 0

Author

Karol A. Penson, May 06 2002

Keywords

• nonn

Comments

Previous name was: Binomial(binomial(n+1,n)^2,n).

Links

• Edward Jiang, Table of n, a(n) for n = 0..100

Programs

Magma

[Binomial((n+1)^2,n) : n in [0..20]]; // Wesley Ivan Hurt, Aug 05 2014

Maple

A070780:=n->binomial((n+1)^2,n): seq(A070780(n),n=0..20); # Wesley Ivan Hurt, Aug 05 2014

Mathematica

Table[Binomial[(n + 1)^2, n], {n, 0, 20}] (* Wesley Ivan Hurt, Aug 05 2014 *)

Maxima

b(n):=sum((binomial(i*n,i-1)*binomial(n^2-i*n,n-i))/i,i,1,n);
makelist(b(n),n,1,10); /* Vladimir Kruchinin, Nov 01 2013 */

PARI

a(n) = binomial((n+1)^2,n); \\ Joerg Arndt, Nov 01 2013

Formula

a(n) = b(n-1) where b(n) = Sum_{i=1..n} binomial(i*n,i-1)*binomial(n^2-i*n,n-i)/i, n>0. - Vladimir Kruchinin, Nov 01 2013

Extensions

New name and more terms from Joerg Arndt, Nov 01 2013