

A061164


a(n) = (20*n)!n!/((10*n)!(7*n)!(4*n)!).


4



1, 5542680, 190818980609400, 7691041400616850556280, 330014847932376708502470210680, 14647137653300940580784413641872332680, 663999280578266939183818080578580843597787800, 30541460340748361003270983719744457382865889296237000
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OFFSET

0,2


COMMENTS

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.


REFERENCES

M. Kontsevich and D. Zagier, Periods, in Mathematics Unlimited  2001 and Beyond, Springer, Berlin, 2001, pp. 771808.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..22
J. W. Bober, Factorial ratios, hypergeometric series, and a family of step functions, 2007, arXiv:0709.1977 [math.NT], J. London Math. Soc., Vol. 79, Issue 2 (2009), 422444.
F. RodriguezVillegas, Integral ratios of factorials and algebraic hypergeometric functions. arXiv:math.NT/0701362


FORMULA

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 RodriguezVillegas).  Peter Bala, Apr 10 2012


MAPLE

A061164 := proc(n)
binomial(20*n, 10*n)*binomial(10*n, 3*n)/binomial(4*n, n) ;
end proc:
seq(A061164(n), n=0..10) ; # R. J. Mathar, oct 26 2011


MATHEMATICA

Table[((20n)!n!)/((10n)!(7n)!(4n)!), {n, 0, 10}] (* Harvey P. Dale, Oct 25 2011 *)


PROG

(MAGMA) [Factorial(20*n)*Factorial(n)/(Factorial(10*n)*Factorial(7*n)*Factorial(4*n)): n in [0..8]]; // Vincenzo Librandi, Oct 26 2011
(PARI) a(n)=(20*n)!*n!/(10*n)!/(7*n)!/(4*n)! \\ Charles R Greathouse IV, Apr 10 2012


CROSSREFS

Cf. A061162, A061163.
Sequence in context: A237973 A204528 A092019 * A250572 A143686 A210011
Adjacent sequences: A061161 A061162 A061163 * A061165 A061166 A061167


KEYWORD

easy,nonn


AUTHOR

Richard Stanley, Apr 17 2001


STATUS

approved



