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a(n) = n-th sept-factorial number divided by 5.
8

%I #42 Dec 20 2022 03:51:28

%S 1,12,228,5928,195624,7824960,367773120,19859748480,1211444657280,

%T 82378236695040,6178367752128000,506626155674496000,

%U 45089727855030144000,4328613874082893824000,445847229030538063872000,49043195193359187025920000,5738053837623024882032640000

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

%H G. C. Greubel, <a href="/A034832/b034832.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 5*a(n) = (7*n-2)(!^7) = Product_{j=1..n} (7*j-2).

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

%F From _Amiram Eldar_, Dec 20 2022: (Start)

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

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

%t Rest[FoldList[Times,1,7*Range[20]-2]/5] (* _Harvey P. Dale_, May 30 2013 *)

%t 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 *)

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

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

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_

%E More terms from _G. C. Greubel_, Feb 22 2018