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A089507 Second column of triangle A089504 and second column of array A078741 divided by 18.

%I A089507 #17 Sep 08 2022 08:45:12
%S A089507 1,30,756,18360,441936,10614240,254788416,6115201920,146766525696,
%T A089507 3522406694400,84537821131776,2028908069959680,48693795855814656,
%U A089507 1168651113600245760,28047626804770062336,673143043784666480640
%N A089507 Second column of triangle A089504 and second column of array A078741 divided by 18.
%C A089507 Convolution of A000400 (powers of 6) with A009968 (powers of 24).
%H A089507 Vincenzo Librandi, <a href="/A089507/b089507.txt">Table of n, a(n) for n = 0..730</a>
%H A089507 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (30,-144).
%F A089507 G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)).
%F A089507 a(n) = A089504(n+2, 2), n>=0.
%F A089507 a(n) = (4*(4*3*2)^n - (3*2*1)^n)/3 = (2^n)*(2^(2*(n+1))-1)*3^(n-1).
%F A089507 a(n) = 6^n*(4^(n+1)-1)/3. - _Vincenzo Librandi_, Oct 18 2017
%t A089507 CoefficientList[Series[1/((1-6x)(1-24x)),{x,0,20}],x] (* or *) LinearRecurrence[{30,-144},{1,30},20] (* _Harvey P. Dale_, Sep 25 2017 *)
%o A089507 (Magma) [6^n*(4^(n+1)-1)/3: n in [0..15]]; // _Vincenzo Librandi_, Oct 18 2017
%Y A089507 Cf. A089505, A089513, A089514.
%K A089507 nonn,easy
%O A089507 0,2
%A A089507 _Wolfdieter Lang_, Dec 01 2003