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A166351 a(n) = (6*n)!/(3*n)!. 2

%I

%S 1,120,665280,17643225600,1295295050649600,202843204931727360000,

%T 58102407620643984998400000,27500101936481280675682713600000,

%U 20007974164906320568399715106816000000

%N a(n) = (6*n)!/(3*n)!.

%C Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem).

%C In Maple notation: a(n)=int(x^n*(1/6)*exp(-(1/4)*x^(1/3))/(sqrt(Pi)*x^(5/6)), x=0..infinity), n=0,1... .

%C This solution is not unique.

%H G. C. Greubel, <a href="/A166351/b166351.txt">Table of n, a(n) for n = 0..100</a>

%F Asymptotics: a(n)=3*sqrt(2)*(1/3-1/(216*n)+1/(31104*n^2)+1003/(33592320*n^3)+ O(1/n^4))*(12^n)^3/(((1/n)^n)^3*(exp(n))^3), n->infinity.

%t Table[(6*n)!/(3*n)!, {n, 0, 25}] (* _G. C. Greubel_, May 10 2016 *)

%o (PARI) a(n) =(6*n)!/(3*n)!; \\ _Michel Marcus_, Aug 17 2013

%K nonn

%O 0,2

%A _Karol A. Penson_, Oct 12 2009

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Last modified September 30 11:58 EDT 2022. Contains 357105 sequences. (Running on oeis4.)