This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061164 #47 Aug 13 2025 13:24:26
%S A061164 1,5542680,190818980609400,7691041400616850556280,
%T A061164 330014847932376708502470210680,
%U A061164 14647137653300940580784413641872332680,663999280578266939183818080578580843597787800,30541460340748361003270983719744457382865889296237000
%N A061164 a(n) = (20*n)!n!/((10*n)!(7*n)!(4*n)!).
%C A061164 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.
%D A061164 M. Kontsevich and D. Zagier, Periods, in Mathematics Unlimited - 2001 and Beyond, Springer, Berlin, 2001, pp. 771-808.
%H A061164 Vincenzo Librandi, <a href="/A061164/b061164.txt">Table of n, a(n) for n = 0..22</a>
%H A061164 Jonathan W. Bober, <a href="http://arxiv.org/abs/0709.1977">Factorial ratios, hypergeometric series, and a family of step functions</a>, arXiv:0709.1977 [math.NT], 2007; J. London Math. Soc., Vol. 79, Issue 2 (2009), 422-444.
%H A061164 M. Kontsevich and D. Zagier, <a href="http://www.ihes.fr/~maxim/TEXTS/Periods.pdf">Periods</a>, Institut des Hautes Etudes Scientifiques 2001 IHES/M/01/22 p. 11.
%H A061164 Fernando Rodriguez Villegas, <a href="http://arxiv.org/abs/math/0701362">Integral ratios of factorials and algebraic hypergeometric functions</a>, arXiv:math/0701362 [math.NT], 2007.
%F A061164 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
%F A061164 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
%F A061164 a(n) ~ 2^(22*n - 1) * 5^(10*n) / (sqrt(Pi*n) * 7^(7*n + 1/2)). - _Vaclav Kotesovec_, Aug 27 2024
%p A061164 A061164 := proc(n)
%p A061164 binomial(20*n,10*n)*binomial(10*n,3*n)/binomial(4*n,n) ;
%p A061164 end proc:
%p A061164 seq(A061164(n),n=0..10) ; # _R. J. Mathar_, Oct 26 2011
%t A061164 Table[((20n)!n!)/((10n)!(7n)!(4n)!),{n,0,10}] (* _Harvey P. Dale_, Oct 25 2011 *)
%o A061164 (Magma) [Factorial(20*n)*Factorial(n)/(Factorial(10*n)*Factorial(7*n)*Factorial(4*n)): n in [0..8]]; // _Vincenzo Librandi_, Oct 26 2011
%o A061164 (PARI) a(n)=(20*n)!*n!/(10*n)!/(7*n)!/(4*n)! \\ _Charles R Greathouse IV_, Apr 10 2012
%Y A061164 Cf. A061162, A061163.
%K A061164 easy,nonn
%O A061164 0,2
%A A061164 _Richard Stanley_, Apr 17 2001