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 A052795 #51 Aug 31 2024 08:30:56
%S A052795 1,1,12,306,12144,657720,45239040,3776965920,371090522880,
%T A052795 41951580652800,5364506808460800,765606216965990400,
%U A052795 120639963305775513600,20803502274492921984000,3896911902445736638464000,787971434323820421362688000,171063718698166603304067072000
%N A052795 a(n) = (6*n)!/(5*n+1)!.
%C A052795 Old name was: A simple grammar.
%H A052795 Seiichi Manyama, <a href="/A052795/b052795.txt">Table of n, a(n) for n = 0..310</a>
%H A052795 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=752">Encyclopedia of Combinatorial Structures 752</a>
%F A052795 E.g.f.: RootOf(-_Z+_Z^6*x+1).
%F A052795 D-finite Recurrence: {a(1)=1, a(2)=12, (-720-9864*n-48600*n^2-110160*n^3-116640*n^4-46656*n^5)*a(n)+(3125*n^4+9375*n^3+10000*n^2+4500*n+720)*a(n+1), a(6)=45239040, a(3)=306, a(4)=12144, a(5)=657720}.
%F A052795 1/25*3^(1/2)*(5+5^(1/2))^(1/2)*(5-5^(1/2))^(1/2)*Pi^(1/2) *GAMMA(2*n+37/3) *GAMMA(2*n+38/3)/GAMMA(n+34/5)/GAMMA(n+33/5)/GAMMA(n+32/5) /GAMMA(n+36/5) *GAMMA(n+13/2)*3125^(-6-n)*2916^(n+6).
%F A052795 a(n) = (6*n)!/(5*n+1)!. - _Mark van Hoeij_, May 29 2013
%F A052795 E.g.f.: exp( 1/6 * Sum_{k>=1} binomial(6*k,k) * x^k/k ). - _Seiichi Manyama_, Feb 08 2024
%F A052795 a(n) = A000142(n)*A002295(n). - _Alois P. Heinz_, Feb 08 2024
%F A052795 From _Seiichi Manyama_, Aug 31 2024: (Start)
%F A052795 E.g.f. satisfies A(x) = 1/(1 - x*A(x)^5).
%F A052795 a(n) = Sum_{k=0..n} (5*n+1)^(k-1) * |Stirling1(n,k)|. (End)
%p A052795 spec := [S,{B=Prod(Z,S,S,S,S,S),S=Sequence(B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); # end of program
%p A052795 seq((6*n)!/(5*n+1)!, n=0..20); # _Mark van Hoeij_, May 29 2013
%o A052795 (PARI) a(n) = (6*n)!/(5*n+1)!; \\ _Joerg Arndt_, May 29 2013
%o A052795 (Python)
%o A052795 from sympy import ff
%o A052795 def A052795(n): return ff(6*n,n-1) # _Chai Wah Wu_, Sep 01 2023
%Y A052795 Cf. A001761, A001763, A365340, A365341.
%Y A052795 Cf. A000142, A002295.
%K A052795 easy,nonn
%O A052795 0,3
%A A052795 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052795 New name using _Mark van Hoeij_'s formula from _Joerg Arndt_, Feb 18 2019
%E A052795 Accidentally removed a(0) reinserted by _Georg Fischer_, May 09 2021