A034829 - OEIS

%I #40 Dec 19 2022 03:45:20

%S 1,9,144,3312,99360,3676320,161758080,8249662080,478480400640,

%T 31101226041600,2239288274995200,176903773724620800,

%U 15213724540317388800,1414876382249517158400,141487638224951715840000,15139177290069833594880000,1725866211067961029816320000

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

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Multifactorials">Multifactorials</a>.

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

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

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

%F D-finite with recurrence: a(n) +(-7*n+5)*a(n-1)=0. - _R. J. Mathar_, Feb 24 2020

%F From _Amiram Eldar_, Dec 19 2022: (Start)

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

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

%t 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 *)

%o (PARI) vector(20, n, prod(j=1, n, 7*j-5)/2) \\ _Michel Marcus_, Jan 07 2015

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

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_