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 A103207 a(n)=(-1)^floor(n/2)/det(M_n) where M_n is the n X n matrix of terms 1/(i+j)! i and j ranging from 1 to n. 1

%I

%S 1,2,144,1036800,1463132160000,668986161758208000000,

%T 148045794139338685651353600000000,

%U 22147346968743318573346465338485637120000000000

%N a(n)=(-1)^floor(n/2)/det(M_n) where M_n is the n X n matrix of terms 1/(i+j)! i and j ranging from 1 to n.

%F a(n)=(1/2^n)*{prod(k=1, n, (2*k)!/k!)}^2.

%F a(n) ~ A * 2^(2*n^2 + 2*n + 5/12) * n^(n^2 + n + 1/12) / exp(3*n^2/2 + n + 1/12), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, May 01 2015

%p seq(mul(mul(k+j,j=1..n), k=0..n), n=0..7); # _Zerinvary Lajos_, Jun 01 2007

%t Table[1/2^n*(Product[(2*k)!/k!,{k,1,n}])^2,{n,0,10}] (* _Vaclav Kotesovec_, May 01 2015 *)

%t Table[2^(2*n^2 + n - 1/12) * Glaisher^3 * BarnesG[n+3/2]^2 / (E^(1/4) * Pi^(n+1/2)),{n,0,10}] (* _Vaclav Kotesovec_, May 01 2015 *)

%o (PARI) a(n)=(1/2^n)*prod(k=1,n,(2*k)!/k!)^2

%Y Cf. A062381.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Mar 19 2005

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Last modified September 24 07:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)