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A081586 Fourth row of Pascal-(1,3,1) array A081578.

%I A081586 #20 Sep 08 2022 08:45:09
%S A081586 1,13,73,245,593,1181,2073,3333,5025,7213,9961,13333,17393,22205,
%T A081586 27833,34341,41793,50253,59785,70453,82321,95453,109913,125765,143073,
%U A081586 161901,182313,204373,228145,253693,281081,310373,341633,374925,410313,447861
%N A081586 Fourth row of Pascal-(1,3,1) array A081578.
%H A081586 Vincenzo Librandi, <a href="/A081586/b081586.txt">Table of n, a(n) for n = 0..10000</a>
%H A081586 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081586 From _Harvey P. Dale_, Nov 06 2011: (Start)
%F A081586 a(n) = (3 + 28*n - 24*n^2 + 32*n^3)/3.
%F A081586 G.f.: (1+3*x)^3/(1-x)^4.
%F A081586 a(0)=1, a(1)=13, a(2)=73, a(3)=245, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%F A081586 E.g.f.: (1/3)*(3 + 36*x + 72*x^2 + 32*x^3)*exp(x). - _G. C. Greubel_, May 26 2021
%t A081586 Table[(3+28n-24n^2+32n^3)/3,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,13,73,245},40] (* _Harvey P. Dale_, Nov 06 2011 *)
%o A081586 (Magma) [(3+28*n-24*n^2+32*n^3)/3: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2011
%o A081586 (Sage) [(3+28*n-24*n^2+32*n^3)/3 for n in (0..40)] # _G. C. Greubel_, May 26 2021
%Y A081586 Cf. A081578, A081585.
%K A081586 easy,nonn
%O A081586 0,2
%A A081586 _Paul Barry_, Mar 23 2003