A051689 - OEIS

A051689

a(n) = (5*n+8)(!^5)/8(!^5), related to A034300 ((5*n+3)(!^5) quintic, or 5-factorials).

%I #14 Sep 08 2022 08:44:59

%S 1,13,234,5382,150696,4972968,188972784,8125829712,390039826176,

%T 20672110787328,1198982425665024,75535892816896512,

%U 5136440711548962816,374960171943074285568,29246893411559794274304

%N a(n) = (5*n+8)(!^5)/8(!^5), related to A034300 ((5*n+3)(!^5) quintic, or 5-factorials).

%C Row m=8 of the array A(6; m,n) := ((5*n+m)(!^5))/m(!^5), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A051689/b051689.txt">Table of n, a(n) for n = 0..352</a>

%F a(n) = ((5*n+8)(!^5))/8(!^5) = A034300(n+2)/8.

%F E.g.f.: 1/(1-5*x)^(13/5).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 12, 5!, 5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(13/5), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-5*x)^(13/5))) \\ _G. C. Greubel_, Aug 15 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^(13/5))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018

%Y Cf. A052562, A008548(n+1), A034323(n+1), A034300(n+1), A034301(n+1), A034325(n+1), A051687-A051691 (rows m=0..10).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_