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

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

Offset

1,2

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

Table of n, a(n) for n=1..7.

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A062407 A212799 A343695 * A047676 A280790 A079187

Adjacent sequences: A097473 A097474 A097475 * A097477 A097478 A097479

Keyword

nonn

Author

Benoit Cloitre, Sep 18 2004

Status

approved