A034833 - OEIS

%I #42 Dec 20 2022 03:51:31

%S 1,13,260,7020,238680,9785880,469722240,25834723200,1601752838400,

%T 110520945849600,8399591884569600,697166126419276800,

%U 62744951377734912000,6086260283640286464000,632971069498589792256000,70259788714343466940416000,8290655068292529098969088000

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

%H Harvey P. Dale, <a href="/A034833/b034833.txt">Table of n, a(n) for n = 1..339</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

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

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

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

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

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

%F Sum_{n>=1} 1/a(n) = 6*(e/7)^(1/7)*(Gamma(6/7) - Gamma(6/7, 1/7)). - _Amiram Eldar_, Dec 20 2022

%t FoldList[Times,1,Rest[7*Range[20]-1]] (* _Harvey P. Dale_, Dec 15 2014 *)

%o (PARI) my(x='x+('x^30)); Vec(serlaplace((-1 + (1-7*x)^(-6/7))/6)) \\ _G. C. Greubel_, Feb 22 2018

%o (Magma) [(&*[(7*k-1): k in [1..n]])/6: n in [1..30]]; // _G. C. Greubel_, Feb 24 2018

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

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_