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A053114 a(n) = ((8*n+9)(!^8))/9, related to A045755 ((8*n+1)(!^8) octo- or 8-factorials). 2

%I

%S 1,17,425,14025,575025,28176225,1606044825,104392913625,7620682694625,

%T 617275298264625,54937501545551625,5328937649918507625,

%U 559538453241443300625,63227845216283092970625

%N a(n) = ((8*n+9)(!^8))/9, related to A045755 ((8*n+1)(!^8) octo- or 8-factorials).

%C Row m=9 of the array A(9; m,n) := ((8*n+m)(!^8))/m(!^8), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A053114/b053114.txt">Table of n, a(n) for n = 0..332</a>

%F a(n) = ((8*n+9)(!^8))/9(!^8) = A045755(n+2)/9.

%F E.g.f.: 1/(1-8*x)^(17/8).

%F G.f.: 1/(1-17x/(1-8x/(1-25x/(1-16x/(1-33x/(1-24x/(1-41x/(1-32x/(1-... (continued fraction). - _Philippe Deléham_, Jan 07 2012

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 16, 5!, 8}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 8*x)^(17/8), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 16 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-8*x)^(17/8))) \\ _G. C. Greubel_, Aug 16 2018

%o (MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-8*x)^(17/8))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A051189, A045755, A034908-12, A034975-6 (rows m=0..8).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_

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Last modified January 20 08:07 EST 2020. Contains 331081 sequences. (Running on oeis4.)