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

1, 11, 198, 4950, 158400, 6177600, 284169600, 15060988800, 903659328000, 60545174976000, 4480342948224000, 362907778806144000, 31935884534940672000, 3033909030819363840000, 309458721143575111680000, 33731000604649687173120000, 3912796070139363712081920000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..339

Index entries for sequences related to factorial numbers.

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

Crossrefs

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

Sequence in context: A186251 A105124 A272500 * A142362 A140534 A377839

Adjacent sequences: A034828 A034829 A034830 * A034832 A034833 A034834

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

More terms added by G. C. Greubel, Feb 23 2018

Status

approved