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

1,2

Links

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

Index entries for sequences related to factorial numbers.

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A325911 A246501 A120977 * A098345 A366299 A361364

Adjacent sequences: A034827 A034828 A034829 * A034831 A034832 A034833

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

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

Status

approved