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Inverse binomial transform of n^2*3^(n-1).
2

%I #9 Dec 28 2019 19:48:36

%S 0,1,10,48,176,560,1632,4480,11776,29952,74240,180224,430080,1011712,

%T 2351104,5406720,12320768,27852800,62521344,139460608,309329920,

%U 682622976,1499463680,3279945728,7147094016,15518924800,33587986432

%N Inverse binomial transform of n^2*3^(n-1).

%C Binomial transform of octagonal numbers A000567. Inverse binomial transform of A069996.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).

%F a(n)=n(3n - 1)2^(n - 2).

%F O.g.f.: -x*(1+4*x)/(-1+2*x)^3. - _R. J. Mathar_, Apr 02 2008

%t LinearRecurrence[{6,-12,8},{0,1,10},30] (* _Harvey P. Dale_, Dec 28 2019 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Jun 09 2003