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A186002 Hankel transform of A186001. 1
1, 1, 2, 16, 768, 294912, 1132462080, 52183852646400, 33664847019245568000, 347485857744891213250560000, 64560982045934655213753964953600000, 239901585047846581083822477336190648320000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..11.

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.

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)

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 December 22 21:10 EST 2014. Contains 252372 sequences.