A034833 a(n) = n-th sept-factorial number divided by 6.

1, 13, 260, 7020, 238680, 9785880, 469722240, 25834723200, 1601752838400, 110520945849600, 8399591884569600, 697166126419276800, 62744951377734912000, 6086260283640286464000, 632971069498589792256000, 70259788714343466940416000, 8290655068292529098969088000

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..339

Index entries for sequences related to factorial numbers.

Formula

a(n) = A049209(n)/6;

a(n) = (7*n-1)(!^7)/6;

a(n) = (1/6)*Product_{j=1..n} (7*j-1);

a(n) = (1/6)*(7*n)! / (7^n * n! * A045754(n) * 2*A034829(n) * 3*A034830(n) * 4*A034831(n) * 5*A034832(n)).

E.g.f.: (-1 + (1-7*x)^(-6/7))/6.

Sum_{n>=1} 1/a(n) = 6*(e/7)^(1/7)*(Gamma(6/7) - Gamma(6/7, 1/7)). - Amiram Eldar, Dec 20 2022

Mathematica

FoldList[Times, 1, Rest[7*Range[20]-1]] (* Harvey P. Dale, Dec 15 2014 *)

Prog

(PARI) my(x='x+('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-6/7))/6)) \\ G. C. Greubel, Feb 22 2018
(Magma) [(&*[(7*k-1): k in [1..n]])/6: n in [1..30]]; // G. C. Greubel, Feb 24 2018

Crossrefs

Cf. A049209, A045754, A034829, A034830, A034831, A034832, A034834.

Sequence in context: A321849 A034242 A142811 * A101004 A340936 A142931

Adjacent sequences: A034830 A034831 A034832 * A034834 A034835 A034836

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved