cp's OEIS Frontend

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.

A034831 a(n) = n-th sept-factorial number divided by 4.

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%I A034831 #39 Dec 20 2022 03:51:36
%S A034831 1,11,198,4950,158400,6177600,284169600,15060988800,903659328000,
%T A034831 60545174976000,4480342948224000,362907778806144000,
%U A034831 31935884534940672000,3033909030819363840000,309458721143575111680000,33731000604649687173120000,3912796070139363712081920000
%N A034831 a(n) = n-th sept-factorial number divided by 4.
%H A034831 G. C. Greubel, <a href="/A034831/b034831.txt">Table of n, a(n) for n = 1..339</a>
%H A034831 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A034831 4*a(n) = (7*n-3)(!^7) = Product_{j=1..n} (7*j-3).
%F A034831 E.g.f.: (-1 + (1-7*x)^(-4/7))/4.
%F A034831 From _Amiram Eldar_, Dec 20 2022: (Start)
%F A034831 a(n) = A144827(n)/4.
%F A034831 Sum_{n>=1} 1/a(n) = 4*(e/7^3)^(1/7)*(Gamma(4/7) - Gamma(4/7, 1/7)). (End)
%t A034831 Drop[With[{nn = 40}, CoefficientList[Series[(-1 + (1 - 7*x)^(-4/7))/4, {x, 0, nn}], x]*Range[0, nn]!], 1] (* _G. C. Greubel_, Feb 22 2018 *)
%t A034831 Table[Product[7 j - 3, {j, n}], {n, 30}]/4 (* _Vincenzo Librandi_, Feb 24 2018 *)
%o A034831 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-4/7))/4)) \\ _G. C. Greubel_, Feb 22 2018
%o A034831 (Magma) [(&*[(7*k-3): k in [1..n]])/4: n in [1..30]]; // _G. C. Greubel_, Feb 24 2018
%Y A034831 Cf. A049209, A045754, A034829, A034830, A034832, A034833, A034834, A144827.
%K A034831 easy,nonn
%O A034831 1,2
%A A034831 _Wolfdieter Lang_
%E A034831 More terms added by _G. C. Greubel_, Feb 23 2018