A061164 a(n) = (20*n)!n!/((10*n)!(7*n)!(4*n)!).

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

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. 771-808.

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, arXiv:0709.1977 [math.NT], 2007; J. London Math. Soc., Vol. 79, Issue 2 (2009), 422-444.

F. Rodriguez-Villegas, Integral ratios of factorials and algebraic hypergeometric functions, arXiv:math.NT/0701362, 2007.

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 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

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