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A081106 6th binomial transform of (1,1,0,0,0,0,...).

%I A081106 #27 Aug 23 2024 22:05:44
%S A081106 1,7,48,324,2160,14256,93312,606528,3919104,25194240,161243136,
%T A081106 1027924992,6530347008,41358864384,261213880320,1645647446016,
%U A081106 10344069660672,64885527871488,406239826673664,2538998916710400,15843353240272896,98716277881700352,614234617930579968
%N A081106 6th binomial transform of (1,1,0,0,0,0,...).
%C A081106 Main diagonal of array defined by m(1,j) = j; m(i,1) = i and m(i,j) = m(i-1,j) + 5*m(i-1,j-1). - _Benoit Cloitre_, Jun 13 2003
%H A081106 Vincenzo Librandi, <a href="/A081106/b081106.txt">Table of n, a(n) for n = 0..300</a>
%H A081106 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).
%F A081106 a(n) = 12*a(n-1) - 36*a(n-2) with n > 1, a(0) = 1, a(1) = 7.
%F A081106 a(n) = (n + 6)*6^(n-1).
%F A081106 G.f.: (1 - 5*x)/(1 - 6*x)^2.
%F A081106 E.g.f.: exp(6*x)*(1 + x). - _Stefano Spezia_, Mar 05 2023
%t A081106 CoefficientList[Series[(1 - 5 x)/(1 - 6 x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)
%t A081106 LinearRecurrence[{12,-36},{1,7},30] (* _Harvey P. Dale_, Nov 07 2013 *)
%o A081106 (Magma) [(n+6)*6^(n-1): n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013
%Y A081106 Cf. A079028, A081105, A006234.
%K A081106 nonn,easy
%O A081106 0,2
%A A081106 _Paul Barry_, Mar 07 2003