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A061164
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a(n) = (20*n)!n!/((10*n)!(7*n)!(4*n)!).
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6
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1, 5542680, 190818980609400, 7691041400616850556280, 330014847932376708502470210680, 14647137653300940580784413641872332680, 663999280578266939183818080578580843597787800, 30541460340748361003270983719744457382865889296237000
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OFFSET
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0,2
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COMMENTS
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According to page 781 of the cited reference the generating function F(x) for a(n) is algebraic but not obviously so and the minimal polynomial satisfied by F(x) is quite large.
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REFERENCES
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M. Kontsevich and D. Zagier, Periods, in Mathematics Unlimited - 2001 and Beyond, Springer, Berlin, 2001, pp. 771-808.
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LINKS
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FORMULA
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One of the 52 sporadic integral factorial ratio sequences found by V. I. Vasyunin (see Bober, Table 2, Entry 43). The o.g.f. sum {n >= 1} a(n)*z^n is an algebraic function over the field of rational functions Q(z) (see Rodriguez-Villegas). - Peter Bala, Apr 10 2012
O.g.f. is a generalized hypergeometric function 8F7([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/7, 2/7, 3/7, 1/2, 4/7, 5/7, 6/7], ((2^22)*(5^10)*x)/7^7). - Karol A. Penson, Apr 11 2022
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MAPLE
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binomial(20*n, 10*n)*binomial(10*n, 3*n)/binomial(4*n, n) ;
end proc:
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MATHEMATICA
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Table[((20n)!n!)/((10n)!(7n)!(4n)!), {n, 0, 10}] (* Harvey P. Dale, Oct 25 2011 *)
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PROG
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(Magma) [Factorial(20*n)*Factorial(n)/(Factorial(10*n)*Factorial(7*n)*Factorial(4*n)): n in [0..8]]; // Vincenzo Librandi, Oct 26 2011
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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