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A124671 Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4, ...)

%I A124671 #26 Feb 08 2022 02:16:28
%S A124671 1,3,7,16,37,85,191,418,893,1871,3863,7892,16005,32297,64959,130374,
%T A124671 261309,523299,1047415,2095800,4192741,8386813,16775167,33552106,
%U A124671 67106237,134214775,268432151,536867228,1073737733,2147479121,4294962303,8589929102,17179863165
%N A124671 Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4, ...)
%H A124671 Vincenzo Librandi, <a href="/A124671/b124671.txt">Table of n, a(n) for n = 1..1000</a>
%H A124671 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F A124671 G.f.: x*(1-3*x+3*x^2)/((1-2*x)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; corrected by _R. J. Mathar_, Sep 16 2009
%F A124671 a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5) for n > 4. - _Vincenzo Librandi_, Mar 15 2014
%F A124671 a(n) = -2 + 2^(1+n) - (5*n)/6 - n^3/6. - _Colin Barker_, Jul 21 2017
%e A124671 a(4) = 16 = sums of 4th row terms of A126277: (1 + 4 + 7 + 4).
%e A124671 a(4) = 16 = 1*1 + 3*2 + 3*2 + 1*3.
%t A124671 CoefficientList[Series[(1 - 3 x + 3 x^2)/((1 - 2 x) (x - 1)^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 15 2014 *)
%o A124671 (PARI) Vec(x*(1-3*x+3*x^2)/((1-2*x)*(x-1)^4) + O(x^100)) \\ _Colin Barker_, Mar 13 2014
%o A124671 (Magma) I:=[1,3,7,16,37]; [n le 5 select I[n] else 6*Self(n-1)-14*Self(n-2)+16*Self(n-3)-9*Self(n-4)+2*Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, Mar 15 2014
%Y A124671 Cf. A126277.
%K A124671 nonn,easy
%O A124671 1,2
%A A124671 _Gary W. Adamson_, Dec 23 2006
%E A124671 More terms from _Colin Barker_, Mar 13 2014