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URL: https://oeis.org/A034831

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A034831
a(n) = n-th sept-factorial number divided by 4.
7
1, 11, 198, 4950, 158400, 6177600, 284169600, 15060988800, 903659328000, 60545174976000, 4480342948224000, 362907778806144000, 31935884534940672000, 3033909030819363840000, 309458721143575111680000, 33731000604649687173120000, 3912796070139363712081920000
OFFSET
1,2
FORMULA
4*a(n) = (7*n-3)(!^7) = Product_{j=1..n} (7*j-3).
E.g.f.: (-1 + (1-7*x)^(-4/7))/4.
From Amiram Eldar, Dec 20 2022: (Start)
a(n) = A144827(n)/4.
Sum_{n>=1} 1/a(n) = 4*(e/7^3)^(1/7)*(Gamma(4/7) - Gamma(4/7, 1/7)). (End)
MATHEMATICA
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 *)
Table[Product[7 j - 3, {j, n}], {n, 30}]/4 (* Vincenzo Librandi, Feb 24 2018 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-4/7))/4)) \\ G. C. Greubel, Feb 22 2018
(Magma) [(&*[(7*k-3): k in [1..n]])/4: n in [1..30]]; // G. C. Greubel, Feb 24 2018
KEYWORD
easy,nonn
EXTENSIONS
More terms added by G. C. Greubel, Feb 23 2018
STATUS
approved