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%I #17 Oct 01 2023 12:07:38
%S 1,6,30,135,567,2268,8748,32805,120285,433026,1535274,5373459,
%T 18600435,63772920,216827928,731794257,2453663097,8178876990,
%U 27119434230,89494132959,294052151151,962352494676,3138105960900,10198844372925
%N Expansion of (-1+1/(1-3*x)^3)/(9*x).
%C G.f. for a(n)=A027472(n+3), n >= 0, is 1/(1-3*x)^3.
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9, -27, 27).
%F a(n) = 3^(n-1)*binomial(n+3, 2); G.f.: (-1+(1-3*x)^(-3))/(x*3^2)=(1-3*x+3*x^2)/(1-3*x)^3.
%F G.f.: F(4,1;2;3x); [From _Paul Barry_, Sep 03 2008]
%F D-finite with recurrence: (n+1)*a(n) +3*(-n-3)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020
%t CoefficientList[Series[((1/(1-3x))^3-1)/(9x),{x,0,30}],x] (* _Harvey P. Dale_, Nov 26 2018 *)
%Y Cf. A001792, A027472. a(n)= A030524(n+1, 1) (first column of triangle).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_