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 A034829 #40 Dec 19 2022 03:45:20 %S A034829 1,9,144,3312,99360,3676320,161758080,8249662080,478480400640, %T A034829 31101226041600,2239288274995200,176903773724620800, %U A034829 15213724540317388800,1414876382249517158400,141487638224951715840000,15139177290069833594880000,1725866211067961029816320000 %N A034829 a(n) = n-th sept-factorial number divided by 2. %H A034829 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Multifactorials">Multifactorials</a>. %H A034829 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>. %F A034829 2*a(n) = (7*n-5)(!^7) = Product_{j=1..n} (7*j-5). %F A034829 E.g.f.: (-1 + (1-7*x)^(-2/7))/2. %F A034829 D-finite with recurrence: a(n) +(-7*n+5)*a(n-1)=0. - _R. J. Mathar_, Feb 24 2020 %F A034829 From _Amiram Eldar_, Dec 19 2022: (Start) %F A034829 a(n) = A084947(n)/2. %F A034829 Sum_{n>=1} 1/a(n) = 2*(e/7^5)^(1/7)*(Gamma(2/7) - Gamma(2/7, 1/7)). (End) %t A034829 Drop[With[{nn = 50}, CoefficientList[Series[(-1 + (1 - 7*x)^(-2/7))/2, {x, 0, nn}], x]*Range[0, nn]!], 1] (* _G. C. Greubel_, Feb 23 2018 *) %o A034829 (PARI) vector(20, n, prod(j=1, n, 7*j-5)/2) \\ _Michel Marcus_, Jan 07 2015 %Y A034829 Cf. A045754, A034830, A034831, A034832, A034833, A034834, A084947. %K A034829 easy,nonn %O A034829 1,2 %A A034829 _Wolfdieter Lang_