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 A186002 Hankel transform of A186001. 2
 1, 1, 2, 16, 768, 294912, 1132462080, 52183852646400, 33664847019245568000, 347485857744891213250560000, 64560982045934655213753964953600000, 239901585047846581083822477336190648320000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..39 FORMULA 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. 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) a(n) ~ 2^(n^2/2) * n^(n^2/2 - 1/12) * Pi^(n/2) / (A * exp(3*n^2/4 - 1/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019 MATHEMATICA Table[2^(1/2*(n - 1)*n)*BarnesG[n + 1], {n, 0, 25}] (* G. C. Greubel, Feb 22 2017 *) CROSSREFS Sequence in context: A015188 A005118 A108400 * A013029 A012915 A012920 Adjacent sequences: A185999 A186000 A186001 * A186003 A186004 A186005 KEYWORD nonn,easy AUTHOR Paul Barry, Feb 09 2011 STATUS approved

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Last modified June 1 03:55 EDT 2023. Contains 363068 sequences. (Running on oeis4.)