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a(n) = n-th sept-factorial number divided by 3.
9

%I #26 Dec 20 2022 03:51:39

%S 1,10,170,4080,126480,4806240,216280800,11246601600,663549494400,

%T 43794266630400,3196981464019200,255758517121536000,

%U 22250990989573632000,2091593153019921408000,211250908455012062208000,22815098113141302718464000,2623736283011249812623360000

%N a(n) = n-th sept-factorial number divided by 3.

%H G. C. Greubel, <a href="/A034830/b034830.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 3*a(n) = (7*n-4)(!^7) = Product_{j=1..n} (7*j-4).

%F E.g.f.: (-1 + (1-7*x)^(-3/7))/3.

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

%F a(n) = A144739(n)/3.

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

%t 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 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-3/7))/3)) \\ _G. C. Greubel_, Feb 23 2018

%Y Cf. A045754, A034829, A034831, A034832, A034833, A034834, A144739.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_

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