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A166351
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a(n) = (6*n)!/(3*n)!.
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2
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1, 120, 665280, 17643225600, 1295295050649600, 202843204931727360000, 58102407620643984998400000, 27500101936481280675682713600000, 20007974164906320568399715106816000000
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OFFSET
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0,2
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COMMENTS
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Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem).
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... .
This solution is not unique.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..100
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FORMULA
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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.
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MATHEMATICA
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Table[(6*n)!/(3*n)!, {n, 0, 25}] (* G. C. Greubel, May 10 2016 *)
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PROG
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(PARI) a(n) =(6*n)!/(3*n)!; \\ Michel Marcus, Aug 17 2013
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CROSSREFS
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Sequence in context: A046987 A127232 A208191 * A147964 A172857 A308327
Adjacent sequences: A166348 A166349 A166350 * A166352 A166353 A166354
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KEYWORD
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nonn
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AUTHOR
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Karol A. Penson, Oct 12 2009
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STATUS
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approved
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