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 A049211 #64 Dec 21 2022 04:46:08
%S A049211 1,8,136,3536,123760,5445440,288608320,17893715840,1270453824640,
%T A049211 101636305971200,9045631231436800,886471860680806400,
%U A049211 94852489092846284800,11002888734770169036800,1375361091846271129600000,184298386307400331366400000,26354669241958247385395200000
%N A049211 a(n) = Product_{k=1..n} (9*k - 1); 9-factorial numbers.
%H A049211 G. C. Greubel, <a href="/A049211/b049211.txt">Table of n, a(n) for n = 0..325</a>
%F A049211 a(n) = 8*A035022(n) = (9*n-1)(!^9), n >= 1, a(0) = 1.
%F A049211 a(n) = (-1)^n*Sum_{k=0..n} 9^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - _Mircea Merca_, May 03 2012
%F A049211 a(n) = 9^n * Gamma(n+8/9) / Gamma(8/9). - _Vaclav Kotesovec_, Jan 28 2015
%F A049211 E.g.f: (1-9*x)^(-8/9). - _Vaclav Kotesovec_, Jan 28 2015
%F A049211 From _Nikolaos Pantelidis_, Dec 09 2020: (Start)
%F A049211 G.f.: 1/(1-8*x-72*x^2/(1-26*x-306*x^2/(1-44*x-702*x^2/(1-62*x-1260*x^2/(1-80*x-1980*x^2/(1-...)))))) (Jacobi continued fraction).
%F A049211 G.f.: 1/(1-8*x/(1-9*x/(1-17*x/(1-18*x/(1-26*x/(1-27*x/(1-35*x/(1-36*x/(1-44*x/(1-45*x/(1-...))))))))))) (Stieltjes continued fraction). (End)
%F A049211 From _Nikolaos Pantelidis_, Dec 19 2020: (Start)
%F A049211 G.f.: 1/G(0) where G(k) = 1 - (18*k+8)*x - 9*(k+1)*(9*k+8)*x^2/G(k+1) (continued fraction).
%F A049211 G.f.: 1/Q(0) where Q(k) = 1 - x*(9*k+8)/(1 - x*(9*k+9)/Q(k+1) ) (continued fraction). (End)
%F A049211 G.f.: hypergeometric2F0([1, 8/9], [--], 9*x). - _G. C. Greubel_, Feb 08 2022
%F A049211 Sum_{n>=0} 1/a(n) = 1 + (e/9)^(1/9)*(Gamma(8/9) - Gamma(8/9, 1/9)). - _Amiram Eldar_, Dec 21 2022
%t A049211 CoefficientList[Series[(1-9*x)^(-8/9),{x,0,20}],x] * Range[0,20]! (* _Vaclav Kotesovec_, Jan 28 2015 *)
%o A049211 (PARI) a(n) = prod(k=1, n, 9*k-1); \\ _Michel Marcus_, Jan 08 2015
%o A049211 (Magma) m:=9; [Round(m^n*Gamma(n +(m-1)/m)/Gamma((m-1)/m)): n in [0..20]]; // _G. C. Greubel_, Feb 08 2022
%o A049211 (Sage) m=9; [m^n*rising_factorial((m-1)/m, n) for n in (0..20)] # _G. C. Greubel_, Feb 08 2022
%Y A049211 Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), A049209 (m=7), A049210 (m=8), this sequence (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).
%Y A049211 Cf. A035022, A048994.
%K A049211 easy,nonn
%O A049211 0,2
%A A049211 _Wolfdieter Lang_
%E A049211 a(9) (originally given incorrectly as 1011636305971200) corrected by _Peter Bala_, Feb 20 2015
%E A049211 a(15)-a(16) from _Vincenzo Librandi_, Feb 20 2015
%E A049211 a(16) corrected and incorrect MAGMA program removed by _Georg Fischer_, May 10 2021