A159783 Hankel transform of ordered Bell numbers A000670. a(n)=det(A000670(i+j-1)), i,j=1,2..n.

1, 4, 192, 221184, 10192158720, 28179280429056000, 6544446260541338419200000, 170229151878929266676890337280000000, 637613431509979741286846928045094207488000000000

Offset

1,2

Links

Todd Silvestri, Table of n, a(n) for n = 1..30

Formula

a(n) = 2^((n-1)*n/2)*G(n+1)*G(n+2)=2^((n-1)*n/2)*A000178(n-1)*A000178(n), where G(n)=product(Gamma(k), k=1..n). - Todd Silvestri, Nov 15 2014

a(n) ~ 2^((n^2 + n + 1)/2) * n^(n^2 + n + 1/3) * Pi^(n + 1/2) / (A^2 * exp(3*n^2/2 + n - 1/6)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015

Mathematica

a[n_Integer/; n>=1]:=2^((n-1) n/2) BarnesG[n+1] BarnesG[n+2] (* Todd Silvestri, Nov 15 2014 *)
a[n_] := Table[HurwitzLerchPhi[1/2, 1-i-j, 0]/2, {i, n}, {j, n}] // Det;
Array[a, 10] (* Jean-François Alcover, Mar 30 2016 *)

Crossrefs

Sequence in context: A299999 A007341 A203516 * A028370 A042127 A219163

Adjacent sequences: A159780 A159781 A159782 * A159784 A159785 A159786

Keyword

nonn

Author

Karol A. Penson, Apr 22 2009

Status

approved