A051687 - OEIS

%I #15 Sep 08 2022 08:44:59

%S 1,11,176,3696,96096,2978976,107243136,4396968576,202260554496,

%T 10315288279296,577656143640576,35237024762075136,2325643634296958976,

%U 165120698035084087296,12549173050666390634496

%N a(n) = (5*n+6)(!^5)/6, related to A008548 ((5*n+1)(!^5) quintic, or 5-factorials).

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

%H G. C. Greubel, <a href="/A051687/b051687.txt">Table of n, a(n) for n = 0..353</a>

%F a(n) = ((5*n+6)(!^5))/6(!^5).

%F E.g.f.: 1/(1-5*x)^(11/5).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 10, 5!, 5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(11/5), {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)^(11/5))) \\ _G. C. Greubel_, Aug 15 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^(11/5))); [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_