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%I #16 Sep 08 2022 08:45:00
%S 1,14,280,7280,232960,8852480,389509120,19475456000,1090625536000,
%T 67618783232000,4598077259776000,340257717223424000,
%U 27220617377873920000,2340973094497157120000,215369524693738455040000
%N a(n) = ((6*n+8)(!^6))/8(!^6), related to A034689 (((6*n+2)(!^6))/2 sextic, or 6-factorials).
%C Row m=7 of the array A(7; m,n) := ((6*n+m)(!^6))/m(!^6), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A053101/b053101.txt">Table of n, a(n) for n = 0..344</a>
%F a(n) = ((6*n+8)(!^6))/8(!^6)= A034689(n+2)/8.
%F E.g.f.: 1/(1-6*x)^(7/3).
%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 13, 5!, 6}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t With[{nn = 30}, CoefficientList[Series[1/(1 - 6*x)^(7/3), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-6*x)^(7/3))) \\ _G. C. Greubel_, Aug 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-6*x)^(7/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018
%Y Cf. A047058, A008542(n+1), A034689(n+1), A034723(n+1), A034724(n+1), A034787(n+1), A034788(n+1), A053100, this sequence, A053102, A053103 (rows m=0..10).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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