A109901 a(n) = binomial(n^2, n*(n+1)/2).

1, 1, 4, 84, 8008, 3268760, 5567902560, 39049918716424, 1118770292985239888, 130276394656770614583240, 61448471214136179596720592960, 117118180539414377821494470432491764, 900390992257782351906806257139068209113040, 27883369051325994219981405855549095749234579210080

Offset: 0

Author

Amarnath Murthy, Jul 14 2005

Keywords

• easy
• nonn

Comments

8*a(2*n+1)^4 = A182010(n) = number of potential group developed cocyclic Hadamard matrices over (the group) Z_{(2*n+1)^2} X Z^2_2 [Baliga, et al., p. 130]. - L. Edson Jeffery, Apr 10 2012

Examples

			a(6) = 36!/(21!*15!) = 5567902560.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• A. Baliga and K. J. Horadam, Cocyclic Hadamard matrices over Z_t X Z^2_2, Australas. J. Combin. 11(1995), 123-134.

Crossrefs

Cf. variants: A014062 (C(n^2,n*(n-1))), A135757 (C(n*(n+1),n*(n+1)/2)).

Cf. A182010.

Programs

Maple

seq(binomial(n^2,n*(n+1)/2),n=0..12); # Emeric Deutsch, Jul 16 2005

Mathematica

Table[Binomial[n^2,(n(n+1))/2],{n,20}] (* Harvey P. Dale, Jun 04 2011 *)

PARI

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

Formula

a(n) = C(n^2, n*(n+1)/2) = (n^2!)/((n(n+1)/2)!*(n(n-1)/2)!).

a(n) = C(n^2, n*(n-1)/2).

Extensions

More terms from Emeric Deutsch, Jul 16 2005

Offset changed to 0 (with a(0)=1), and name changed slightly by Paul D. Hanna, Jun 24 2011

Terms a(12) and beyond from Andrew Howroyd, Nov 09 2019