A091810 Hankel transform of the sequence A001469 (unsigned), Genocchi numbers of first kind.

1, 2, 96, 497664, 825564856320, 1027134771639091200000, 1932215036193527461576704000000000, 9973959265081827837426668870219857920000000000000

Offset

0,2

Comments

This sequence is the Hankel transform (see A001906 for definition)of the sequence defined by, for n>=0, a(n) = |A001469(n+1)|; example: det([1, 1, 3, 17; 1, 3, 17, 155; 3, 17, 155, 2073; 17, 155, 2073, 38227]) = 497664 = 4!*12^4.

Links

G. C. Greubel, Table of n, a(n) for n = 0..24

Formula

a(n) = (n+1)!*A000178(n)^4 = (n+1)!*A055209(n)^2.

Mathematica

Table[(n + 1)!*BarnesG[n + 2]^4, {n, 0, 10}] (* G. C. Greubel, Oct 14 2018 *)

Prog

(PARI) for(n=0, 10, print1((n+1)!*(prod(k=0, n, (k!)^2))^2, ", ")) \\ G. C. Greubel, Oct 14 2018
(Magma) [Factorial(n+1)*(&*[(Factorial(k))^2: k in [0..n]])^2: n in [0..10]]; // G. C. Greubel, Oct 14 2018

Crossrefs

Cf. A000178 A001469 A001906 A055209.

Sequence in context: A036980 A337653 A168442 * A344662 A165642 A057528

Adjacent sequences: A091807 A091808 A091809 * A091811 A091812 A091813

Keyword

nonn

Author

Philippe Deléham, Mar 07 2004

Status

approved