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%I #19 Sep 08 2022 08:45:00
%S 1,13,247,6175,191425,7082725,304557175,14923301575,820781586625,
%T 50067676784125,3354534344536375,244881007151155375,
%U 19345599564941274625,1644375963020008343125,149638212634820759224375
%N a(n) = ((6*n+7)(!^6))/7, related to A008542 ((6*n+1)(!^6) 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="/A053100/b053100.txt">Table of n, a(n) for n = 0..344</a>
%F a(n) = ((6*n+7)(!^6))/7(!^6) = A008542(n+2)/7.
%F E.g.f.: 1/(1-6*x)^(13/6).
%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 12, 5!, 6}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t With[{nn=20},CoefficientList[Series[1/(1-6x)^(13/6),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 20 2015 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-6*x)^(13/6))) \\ _G. C. Greubel_, Aug 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-6*x)^(13/6))); [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), this sequence, A053101, A053102, A053103 (rows m=0..10).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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