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 A034830 #26 Dec 20 2022 03:51:39 %S A034830 1,10,170,4080,126480,4806240,216280800,11246601600,663549494400, %T A034830 43794266630400,3196981464019200,255758517121536000, %U A034830 22250990989573632000,2091593153019921408000,211250908455012062208000,22815098113141302718464000,2623736283011249812623360000 %N A034830 a(n) = n-th sept-factorial number divided by 3. %H A034830 G. C. Greubel, <a href="/A034830/b034830.txt">Table of n, a(n) for n = 1..339</a> %H A034830 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>. %F A034830 3*a(n) = (7*n-4)(!^7) = Product_{j=1..n} (7*j-4). %F A034830 E.g.f.: (-1 + (1-7*x)^(-3/7))/3. %F A034830 From _Amiram Eldar_, Dec 20 2022: (Start) %F A034830 a(n) = A144739(n)/3. %F A034830 Sum_{n>=1} 1/a(n) = 3*(e/7^4)^(1/7)*(Gamma(3/7) - Gamma(3/7, 1/7)). (End) %t A034830 Drop[With[{nn = 40}, CoefficientList[Series[(-1 + (1 - 7*x)^(-3/7))/3, {x, 0, nn}], x]*Range[0, nn]!], 1] (* _G. C. Greubel_, Feb 23 2018 *) %o A034830 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-3/7))/3)) \\ _G. C. Greubel_, Feb 23 2018 %Y A034830 Cf. A045754, A034829, A034831, A034832, A034833, A034834, A144739. %K A034830 easy,nonn %O A034830 1,2 %A A034830 _Wolfdieter Lang_ %E A034830 More terms added by _G. C. Greubel_, Feb 23 2018