A112332 a(n) = Product_{k=0..n-1} k!*binomial(2k,k).
1, 1, 2, 24, 2880, 4838400, 146313216000, 97339256340480000, 1683704371913057894400000, 873705178746128941669416960000000, 15414977576506278044562764045746176000000000, 10334857226047177887548812577909403133201612800000000000
Offset: 0
Programs
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Maple
seq(mul(mul((j+k),j=1..k), k=1..n), n=-1..9); # Zerinvary Lajos, Sep 21 2007
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Mathematica
Table[Product[(2*k)!/k!,{k,0,n-1}],{n,0,10}] (* Vaclav Kotesovec, Jul 11 2015 *)
Formula
a(n)=denominator(Product{k=0..n-1, (2k+1)!/(n+k)!}).
G.f.: 1+ x*G(0)/2, where G(k)= 1 + 1/(1 - 1/(1 + 1/((2*k+2)!/(k+1)!)/x/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 15 2013
a(n) ~ A^(1/2) * 2^(n^2 - n/2 - 7/24) * n^(n^2/2 - n/2 + 1/24) / exp(3*n^2/4 - n/2 + 1/24), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 11 2015
From Alois P. Heinz, Jun 30 2022: (Start)
a(n) = Product_{i=1..n-1} Product_{j=i..n-1} (i+j).
a(n) = A110131(n). (End)