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a(n)=Product{k=0..n, (2*k+0^k)^(n-k)}; a(n+1)=2^C(n+1,2)*Product(k!,k,1,n)=A000178(n)*A006125(n+1).
Essentially the same as A108400.
Contribution from Alexander R. Povolotsky, Feb 10 2011: (Start)
WolframAlpha shows that
a(n) = (0^n*2^(1/2*(n-1)*n)*exp^(1/12-zeta^(1, 0)(-1, n+1)))/A
where zeta(s, a)is the generalized Riemann zeta function and A is the Glaisher‐Kinkelin constant.
WolframAlpha suggests that for all terms given
a(n) = 2^(1/2*(n-1)*n)*G(n+1)
where G(n) is the Barnes G-function. (End)
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