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Expansion of e.g.f. (1+3*x)/(1-3*x).
2

%I #26 Feb 02 2023 05:05:42

%S 1,6,36,324,3888,58320,1049760,22044960,529079040,14285134080,

%T 428554022400,14142282739200,509122178611200,19855764965836800,

%U 833942128565145600,37527395785431552000,1801314997700714496000,91867064882736439296000,4960821503667767721984000

%N Expansion of e.g.f. (1+3*x)/(1-3*x).

%H Vincenzo Librandi, <a href="/A098559/b098559.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = 6 * A034001(n) for n >= 1.

%F a(n) = 2*3^n*n! - 0^n.

%F Sum_{n>=0} 1/a(n) = (exp(1/3)+1)/2. - _Amiram Eldar_, Feb 02 2023

%t Join[{1},Table[2*3^n n!,{n,20}]] (* _Harvey P. Dale_, Aug 08 2014 *)

%o (Magma) [2*3^n*Factorial(n)-0^n: n in [0..20]]; // _Vincenzo Librandi_, Aug 08 2014

%Y Cf. A098558, A032184.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 14 2004