A034830 a(n) = n-th sept-factorial number divided by 3.

1, 10, 170, 4080, 126480, 4806240, 216280800, 11246601600, 663549494400, 43794266630400, 3196981464019200, 255758517121536000, 22250990989573632000, 2091593153019921408000, 211250908455012062208000, 22815098113141302718464000, 2623736283011249812623360000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..339
• Index entries for sequences related to factorial numbers.

Crossrefs

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

Programs

Mathematica

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 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-3/7))/3)) \\ G. C. Greubel, Feb 23 2018

Formula

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

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

From Amiram Eldar, Dec 20 2022: (Start)

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

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

Extensions

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