A097476 a(n) = Product_{i=0..n-1} ((2i)!)^2.

1, 4, 2304, 1194393600, 1941728542064640000, 25569049282962188245401600000000, 5866627428836325123819714259080708096000000000000

Offset: 1

Author

Benoit Cloitre, Sep 18 2004

Keywords

• nonn

Comments

a(n) = determinant of n X n matrix m(i,j)=E(2i+2j), 0<=i,j<=n-1, where E(2k) is the (2k)-th signless Euler number in 1/cos(z) = Sum_{k>=0} E(2k)*z^(2k)/(2k)!.

References

• C. Krattenthaler, Advanced Determinant Calculus, p. 46

Links

• C. Krattenthaler, Advanced Determinant Calculus, Séminaire Lotharingien Combin. 42 ("The Andrews Festschrift") (1999), Article B42q, 67 pp.

Programs

Mathematica

Table[Product[((2i)!)^2,{i,0,n-1}],{n,8}] (* Harvey P. Dale, Jul 05 2021 *)

PARI

a(n)=prod(i=0,n-1,((2*i)!)^2)