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%I #21 Sep 08 2022 08:45:00
%S 1,18,468,15912,668304,33415200,1938081600,127913385600,9465590534400,
%T 776178423820800,69856058143872000,6845893698099456000,
%U 725664731998542336000,82725779447833826304000
%N a(n) = ((8*n+10)(!^8))/20, related to A034908 ((8*n+2)(!^8) octo- or 8-factorials).
%C Row m=10 of the array A(9; m,n) := ((8*n+m)(!^8))/m(!^8), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A053115/b053115.txt">Table of n, a(n) for n = 0..332</a>
%F a(n) = ((8*n+10)(!^8))/10(!^8) = A034908(n+2)/10.
%F E.g.f.: 1/(1-8*x)^(9/4).
%F G.f.: 1/(1-18x/(1-8x/(1-26x/(1-16x/(1-34x/(1-24x/(1-42x/(1-32x/(1-... (continued fraction). - _Philippe Deléham_, Jan 07 2012
%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 17, 5!, 8}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t With[{nmax = 50}, CoefficientList[Series[1/(1 - 8*x)^(9/4), {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Aug 26 2018 *)
%o (PARI) x='x+O('x^25); Vec(serlaplace(1/(1-8*x)^(9/4))) \\ _G. C. Greubel_, Aug 26 2018
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-8*x)^(9/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 26 2018
%Y Cf. A051189, A045755, A034908-12, A034975-6, A053114 (rows m=0..9).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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