A034832 a(n) = n-th sept-factorial number divided by 5.

1, 12, 228, 5928, 195624, 7824960, 367773120, 19859748480, 1211444657280, 82378236695040, 6178367752128000, 506626155674496000, 45089727855030144000, 4328613874082893824000, 445847229030538063872000, 49043195193359187025920000, 5738053837623024882032640000

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

5*a(n) = (7*n-2)(!^7) = Product_{j=1..n} (7*j-2).

E.g.f.: (-1 + (1-7*x)^(-5/7))/5.

From Amiram Eldar, Dec 20 2022: (Start)

a(n) = A147585(n+1)/5.

Sum_{n>=1} 1/a(n) = 5*(e/7^2)^(1/7)*(Gamma(5/7) - Gamma(5/7, 1/7)). (End)

Mathematica

Rest[FoldList[Times, 1, 7*Range[20]-2]/5] (* Harvey P. Dale, May 30 2013 *)
Drop[With[{nn = 50}, CoefficientList[Series[(-1 + (1 - 7*x)^(-5/7))/5, {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 22 2018 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-5/7))/5)) \\ G. C. Greubel, Feb 22 2018

Crossrefs

Cf. A045754, A034829, A034830, A034831, A034833, A034834, A084947, A147585.

Sequence in context: A337332 A290754 A318417 * A231448 A221657 A089370

Adjacent sequences: A034829 A034830 A034831 * A034833 A034834 A034835

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

More terms from G. C. Greubel, Feb 22 2018

Status

approved