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 A049212 #43 Dec 22 2022 04:15:35
%S A049212 1,9,171,4959,193401,9476649,559122291,38579438079,3047775608241,
%T A049212 271252029133449,26853950884211451,2927080646379048159,
%U A049212 348322596919106730921,44933615002564768288809,6245772485356502792144451,930620100318118916029523199,147968595950580907648694188641
%N A049212 a(n) = -Product_{k=0..n} (10*k - 1); deca-factorial numbers.
%H A049212 Andrew Howroyd, <a href="/A049212/b049212.txt">Table of n, a(n) for n = 0..100</a>
%H A049212 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A049212 a(n) = 9*A035278(n) = (10*n-1)(!^10), n >= 1, a(0) = 1.
%F A049212 a(n) = (-1)^n*Sum_{k=0..n} 10^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 A049212 a(n) = 10^n * Gamma(n+9/10) / Gamma(9/10). - _Vaclav Kotesovec_, Jan 28 2015
%F A049212 E.g.f.: (1-10*x)^(-9/10). - _Vaclav Kotesovec_, Jan 28 2015
%F A049212 From _Nikolaos Pantelidis_, Jan 17 2021: (Start)
%F A049212 G.f.: 1/G(0) where G(k) = 1 - (20*k+9)*x - 10*(k+1)*(10*k+9)*x^2/G(k+1) (continued fraction).
%F A049212 G.f.: 1/(1-9*x-90*x^2/(1-29*x-380*x^2/(1-49*x-870*x^2/(1-69*x-1560*x^2/(1-89*x-2450*x^2/(1-...)))))) (Jacobi continued fraction).
%F A049212 G.f.: 1/Q(0) where Q(k) = 1 - x*(10*k+9)/(1 - x*(10*k+10)/Q(k+1)) (continued fraction).
%F A049212 G.f.: 1/(1-9*x/(1-10*x/(1-19*x/(1-20*x/(1-29*x/(1-30*x/(1-39*x/(1-40*x/(1-49*x/(1-50*x/(1-...))))))))))) (Stieltjes continued fraction).
%F A049212 (End)
%F A049212 G.f.: Hypergeometric2F0([1, 9/10], --; 10*x). - _G. C. Greubel_, Feb 03 2022
%F A049212 Sum_{n>=0} 1/a(n) = 1 + (e/10)^(1/10)*(Gamma(9/10) - Gamma(9/10, 1/10)). - _Amiram Eldar_, Dec 22 2022
%t A049212 CoefficientList[Series[(1-10*x)^(-9/10),{x,0,20}],x] * Range[0,20]! (* _Vaclav Kotesovec_, Jan 28 2015 *)
%o A049212 (PARI) a(n) = {-prod(k=0, n, 10*k-1)} \\ _Andrew Howroyd_, Jan 02 2020
%o A049212 (Magma) [Round(10^n*Gamma(n+9/10)/Gamma(9/10)): n in [0..25]]; // _G. C. Greubel_, Feb 03 2022
%o A049212 (Sage) [10^n*rising_factorial(9/10, n) for n in (0..25)] # _G. C. Greubel_, Feb 03 2022
%Y A049212 Cf. A008543, A035278, A048994, A049209, A049210, A049211, A048176.
%K A049212 easy,nonn
%O A049212 0,2
%A A049212 _Wolfdieter Lang_
%E A049212 Terms a(14) and beyond from _Andrew Howroyd_, Jan 02 2020