A070780 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

0,2

Comments

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

Links

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

Formula

a(n)=b(n-1), 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]

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 *)

Prog

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

Crossrefs

Sequence in context: A294359 A336639 A178184 * A132687 A364152 A238844

Adjacent sequences: A070777 A070778 A070779 * A070781 A070782 A070783

Keyword

nonn

Author

Karol A. Penson, May 06 2002

Extensions

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

Status

approved