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A159783 Hankel transform of ordered Bell numbers A000670. a(n)=det(A000670(i+j-1)), i,j=1,2..n. 1
1, 4, 192, 221184, 10192158720, 28179280429056000, 6544446260541338419200000, 170229151878929266676890337280000000, 637613431509979741286846928045094207488000000000 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)