A101799 a(n)= det[A000522(i+j+1)], i,j=0...n, is the Hankel determinant of order n+1 of the arrangements numbers, s. A000522; a(n) = product( (p!)^2,p=0..n )*(n+1)!*LaguerreL(n+1,0,-1), n=0,1..., where LaguerreL(n,lambda,x) are generalized Laguerre polynomials; a(n)=A055209(n)*A002720(n+1);.

2, 7, 136, 30096, 128231424, 15917683507200, 81063451589345280000, 22675515428700722036736000000, 449302248871829829537656890982400000000, 790103237429135552913731284331032467210240000000000

Offset

0,1

Links

Table of n, a(n) for n=0..9.

Formula

a(n) ~ 2^(n+1/2) * Pi^(n+1) * n^(n^2 + 3*n + 25/12) / (A^2 * exp(3*n^2/2 + 3*n - 2*sqrt(n) + 1/3)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, May 11 2021

Mathematica

a[n_] := Det[Table[E*Gamma[i+j+2, 1] // FunctionExpand, {i, 0, n}, {j, 0, n}]];
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, May 23 2016 *)
Table[BarnesG[n+2]^2 * (n+1)! * LaguerreL[n+1, 0, -1], {n, 0, 12}] (* Vaclav Kotesovec, May 11 2021 *)

Crossrefs

Cf. A000522, A055209, A002720.

Sequence in context: A286423 A041727 A120379 * A201172 A062617 A207139

Adjacent sequences: A101796 A101797 A101798 * A101800 A101801 A101802

Keyword

nonn

Author

Karol A. Penson, Dec 16 2004

Status

approved