%I #39 Dec 20 2022 03:51:36

%S 1,11,198,4950,158400,6177600,284169600,15060988800,903659328000,

%T 60545174976000,4480342948224000,362907778806144000,

%U 31935884534940672000,3033909030819363840000,309458721143575111680000,33731000604649687173120000,3912796070139363712081920000

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

%H G. C. Greubel, <a href="/A034831/b034831.txt">Table of n, a(n) for n = 1..339</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

%F 4*a(n) = (7*n-3)(!^7) = Product_{j=1..n} (7*j-3).

%F E.g.f.: (-1 + (1-7*x)^(-4/7))/4.

%F From _Amiram Eldar_, Dec 20 2022: (Start)

%F a(n) = A144827(n)/4.

%F Sum_{n>=1} 1/a(n) = 4*(e/7^3)^(1/7)*(Gamma(4/7) - Gamma(4/7, 1/7)). (End)

%t 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 Table[Product[7 j - 3, {j, n}], {n, 30}]/4 (* _Vincenzo Librandi_, Feb 24 2018 *)

%o (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-4/7))/4)) \\ _G. C. Greubel_, Feb 22 2018

%o (Magma) [(&*[(7*k-3): k in [1..n]])/4: n in [1..30]]; // _G. C. Greubel_, Feb 24 2018

%Y Cf. A049209, A045754, A034829, A034830, A034832, A034833, A034834, A144827.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_

%E More terms added by _G. C. Greubel_, Feb 23 2018