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 A034832 #42 Dec 20 2022 03:51:28 %S A034832 1,12,228,5928,195624,7824960,367773120,19859748480,1211444657280, %T A034832 82378236695040,6178367752128000,506626155674496000, %U A034832 45089727855030144000,4328613874082893824000,445847229030538063872000,49043195193359187025920000,5738053837623024882032640000 %N A034832 a(n) = n-th sept-factorial number divided by 5. %H A034832 G. C. Greubel, <a href="/A034832/b034832.txt">Table of n, a(n) for n = 1..339</a> %H A034832 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>. %F A034832 5*a(n) = (7*n-2)(!^7) = Product_{j=1..n} (7*j-2). %F A034832 E.g.f.: (-1 + (1-7*x)^(-5/7))/5. %F A034832 From _Amiram Eldar_, Dec 20 2022: (Start) %F A034832 a(n) = A147585(n+1)/5. %F A034832 Sum_{n>=1} 1/a(n) = 5*(e/7^2)^(1/7)*(Gamma(5/7) - Gamma(5/7, 1/7)). (End) %t A034832 Rest[FoldList[Times,1,7*Range[20]-2]/5] (* _Harvey P. Dale_, May 30 2013 *) %t A034832 Drop[With[{nn = 50}, CoefficientList[Series[(-1 + (1 - 7*x)^(-5/7))/5, {x, 0, nn}], x]*Range[0, nn]!], 1] (* _G. C. Greubel_, Feb 22 2018 *) %o A034832 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-5/7))/5)) \\ _G. C. Greubel_, Feb 22 2018 %Y A034832 Cf. A045754, A034829, A034830, A034831, A034833, A034834, A084947, A147585. %K A034832 easy,nonn %O A034832 1,2 %A A034832 _Wolfdieter Lang_ %E A034832 More terms from _G. C. Greubel_, Feb 22 2018