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 A049209 #76 Dec 19 2022 01:59:47
%S A049209 1,6,78,1560,42120,1432080,58715280,2818333440,155008339200,
%T A049209 9610517030400,663125675097600,50397551307417600,4182996758515660800,
%U A049209 376469708266409472000,36517561701841718784000,3797826416991538753536000,421558732286060801642496000
%N A049209 a(n) = -Product_{k=0..n} (7*k-1); sept-factorial numbers.
%H A049209 G. C. Greubel, <a href="/A049209/b049209.txt">Table of n, a(n) for n = 0..330</a>
%H A049209 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A049209 a(n) = 6*A034833(n) = (7*n-1)*(!^7), n >= 1, a(0) := 1.
%F A049209 a(n) = Product_{k=1..n} (7*k - 1). a(0) = 1; a(n) = (7*n - 1)*a(n-1) for n > 0. - _Klaus Brockhaus_, Nov 10 2008
%F A049209 G.f.: 1/(1-6*x/(1-7*x/(1-13*x/(1-14*x/(1-20*x/(1-21*x/(1-27*x/(1-28*x/(1-...(continued fraction). - _Philippe Deléham_, Jan 08 2012
%F A049209 a(n) = (-1)^n*Sum_{k=0..n} 7^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 A049209 a(n) = 7^n * Gamma(n+6/7) / Gamma(6/7). - _Vaclav Kotesovec_, Jan 28 2015
%F A049209 E.g.f.: (1-7*x)^(-6/7). - _Vaclav Kotesovec_, Jan 28 2015
%F A049209 From _Nikolaos Pantelidis_, Dec 19 2020: (Start)
%F A049209 G.f.: 1/G(0) where G(k) = 1 - (14*k+6)*x - 7*(k+1)*(7*k+6)*x^2/G(k+1); (continued fraction).
%F A049209 which starts as 1/(1-6*x-42*x^2/(1-20*x-182*x^2/(1-34*x-420*x^2/(1-48*x-756*x^2/(1-62*x-1190*x^2/(1-... )))))) (Jacobi continued fraction).
%F A049209 G.f.: 1/Q(0) where Q(k) = 1 - (7*k+6)*x/(1 - (7*k+7)*x/Q(k+1) ); (continued fraction). (End)
%F A049209 Sum_{n>=0} 1/a(n) = 1 + (e/7)^(1/7)*(Gamma(6/7) - Gamma(6/7, 1/7)). - _Amiram Eldar_, Dec 19 2022
%t A049209 CoefficientList[Series[(1-7*x)^(-6/7),{x,0,20}],x] * Range[0,20]! (* _Vaclav Kotesovec_, Jan 28 2015 *)
%t A049209 With[{m=7}, Table[m^n*Pochhammer[(m-1)/m, n], {n, 0, 30}]] (* _G. C. Greubel_, Feb 16 2022 *)
%o A049209 (Magma) [ -&*[ (7*k-1): k in [0..n-1] ]: n in [1..15] ]; // _Klaus Brockhaus_, Nov 10 2008
%o A049209 (Sage) m=7; [m^n*rising_factorial((m-1)/m, n) for n in (0..30)] # _G. C. Greubel_, Feb 16 2022
%Y A049209 Cf. A034833, A045754, A048994, A051188, A084947, A144739, A144827, A147585.
%Y A049209 Row sums of triangle A051186 (scaled Stirling1 triangle).
%Y A049209 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), this sequence (m=7), A049210 (m=8), A049211 (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).
%K A049209 easy,nonn
%O A049209 0,2
%A A049209 _Wolfdieter Lang_