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%I #18 Sep 08 2022 08:45:00
%S 1,16,368,11040,408480,17973120,916629120,53164488960,3455691782400,
%T 248809808332800,19655974858291200,1690413837813043200,
%U 157208486916613017600,15720848691661301760000
%N a(n) = ((7*n+9)(!^7))/9(!^7), related to A034829 (((7*n+2)(!^7))/2 sept-, or 7-factorials).
%C Row m=9 of the array A(8; m,n) := ((7*n+m)(!^7))/m(!^7), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A053105/b053105.txt">Table of n, a(n) for n = 0..337</a>
%F a(n) = ((7*n+9)(!^7))/9(!^7)= A034829(n+2)/9.
%F E.g.f.: 1/(1-7*x)^(16/7).
%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 15, 5!, 7}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t CoefficientList[Series[1/(1-7x)^(16/7),{x,0,20}],x]Range[0,20]! (* _Harvey P. Dale_, Sep 11 2011 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-7*x)^(16/7))) \\ _G. C. Greubel_, Aug 16 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-7*x)^(16/7))); [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_
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