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

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

Offset: 0

Author

Philippe Deléham, Mar 07 2004

Keywords

• nonn

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

Crossrefs

Cf. A000178 A001469 A001906 A055209.

Programs

Magma

[Factorial(n+1)*(&*[(Factorial(k))^2: k in [0..n]])^2: n in [0..10]]; // G. C. Greubel, Oct 14 2018

Mathematica

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

PARI

for(n=0,10, print1((n+1)!*(prod(k=0,n, (k!)^2))^2, ", ")) \\ G. C. Greubel, Oct 14 2018

Formula

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