A034829 a(n) = n-th sept-factorial number divided by 2.

1, 9, 144, 3312, 99360, 3676320, 161758080, 8249662080, 478480400640, 31101226041600, 2239288274995200, 176903773724620800, 15213724540317388800, 1414876382249517158400, 141487638224951715840000, 15139177290069833594880000, 1725866211067961029816320000

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Peter Luschny, Multifactorials.

Index entries for sequences related to factorial numbers.

Formula

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

E.g.f.: (-1 + (1-7*x)^(-2/7))/2.

D-finite with recurrence: a(n) +(-7*n+5)*a(n-1)=0. - R. J. Mathar, Feb 24 2020

From Amiram Eldar, Dec 19 2022: (Start)

a(n) = A084947(n)/2.

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

Mathematica

Drop[With[{nn = 50}, CoefficientList[Series[(-1 + (1 - 7*x)^(-2/7))/2, {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 23 2018 *)

Prog

(PARI) vector(20, n, prod(j=1, n, 7*j-5)/2) \\ Michel Marcus, Jan 07 2015

Crossrefs

Cf. A045754, A034830, A034831, A034832, A034833, A034834, A084947.

Sequence in context: A325173 A067415 A069134 * A162993 A094594 A173213

Adjacent sequences: A034826 A034827 A034828 * A034830 A034831 A034832

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved