%I #16 Sep 08 2022 08:45:00

%S 1,19,532,19684,905464,49800520,3187233280,232668029440,

%T 19078778414080,1736168835681280,173616883568128000,

%U 18924240308925952000,2233060356453262336000,283598665269564316672000

%N a(n) = ((9*n+10)(!^9))/10, related to A045756 ((9*n+1)(!^9) 9-factorials).

%C Row m=10 of the array A(10; m,n) := ((9*n+m)(!^9))/m(!^9), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A053116/b053116.txt">Table of n, a(n) for n = 0..327</a>

%F a(n) = ((9*n+10)(!^9))/10(!^9) = A045756(n+2)/10.

%F E.g.f.: 1/(1-9*x)^(19/9).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 18, 3*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nmax = 50}, CoefficientList[Series[1/(1 - 9*x)^(19/9), {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Aug 26 2018 *)

%o (PARI) x='x+O('x^25); Vec(serlaplace(1/(1 - 9*x)^(19/9))) \\ _G. C. Greubel_, Aug 26 2018

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1 - 9*x)^(19/9))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 26 2018

%Y Cf. A051232, A045756, A035012-3, A035017-8, A035020-3 (rows m=0..9).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_