%I #15 Sep 08 2022 08:45:00

%S 1,15,330,9570,344520,14814360,740718000,42220926000,2702139264000,

%T 191851887744000,14964447244032000,1271978015742720000,

%U 117021977448330240000,11585175767384693760000

%N a(n) = ((7*n+8)(!^7))/8, related to A045754 ((7*n+1)(!^7) sept-, or 7-factorials).

%C Row m=8 of the array A(8; m,n) := ((7*n+m)(!^7))/m(!^7), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A053104/b053104.txt">Table of n, a(n) for n = 0..337</a>

%F a(n) = ((7*n+8)(!^7))/8(!^7) = A045754(n+2)/8.

%F E.g.f.: 1/(1-7*x)^(15/7).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 14, 5!, 7}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 7*x)^(15/7), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 16 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-7*x)^(15/7))) \\ _G. C. Greubel_, Aug 16 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-7*x)^(15/7))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A051188, A045754(n+1), A034829-34(n+1), A053104-A053106 (rows m=0..10).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_