%I #17 Sep 08 2022 08:45:00

%S 1,17,408,12648,480624,21628080,1124660160,66354949440,4379426663040,

%T 319698146401920,25575851712153600,2225099098957363200,

%U 209159315301992140800,21125090845501206220800

%N a(n) = ((7*n+10)(!^7))/10(1^7), related to A034830 (((7*n+3)(!^7))/3 sept-, or 7-factorials).

%C Row m=10 of the array A(8; m,n) := ((7*n+m)(!^7))/m(!^7), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A053106/b053106.txt">Table of n, a(n) for n = 0..337</a>

%F a(n) = ((7*n+10)(!^7))/10(!^7) = A034830(n+2)/10.

%F E.g.f.: 1/(1-7*x)^(17/7).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 16, 5!, 7}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 7*x)^(17/7), {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)^(17/7))) \\ _G. C. Greubel_, Aug 16 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-7*x)^(17/7))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A051188, A045754(n+1), A034829-A034834(n+1), A053104-A053106 (rows m=0..10).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_