%I #21 Sep 18 2024 16:17:29
%S 1,13,79,307,886,2086,4258,7834,13327,21331,32521,47653,67564,93172,
%T 125476,165556,214573,273769,344467,428071,526066,640018,771574,
%U 922462,1094491,1289551,1509613,1756729,2033032,2340736,2682136,3059608
%N Fourth row of Pascal-(1,2,1) array A081577.
%C Equals binomial transform of [1, 12, 54, 108, 81, 0, 0, 0, ...] where (1, 12, 54, 108, 81) = row 4 of triangle A013610. - _Gary W. Adamson_, Jul 19 2008
%H Vincenzo Librandi, <a href="/A081584/b081584.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (8 + 6*n + 81*n^2 - 18*n^3 + 27*n^4)/8.
%F G.f.: (1+2*x)^4/(1-x)^5.
%F E.g.f.: (1/8)*(8 + 96*x + 216*x^2 + 144*x^3 + 27*x^4)*exp(x). - _G. C. Greubel_, May 26 2021
%p seq((8+6*n+81*n^2-18*n^3+27*n^4)/8, n=0..40); # _G. C. Greubel_, May 26 2021
%t CoefficientList[Series[(1+2x)^4/(1-x)^5, {x,0,40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%t LinearRecurrence[{5,-10,10,-5,1},{1,13,79,307,886},40] (* _Harvey P. Dale_, Sep 18 2024 *)
%o (Magma) [(8+6*n+81*n^2-18*n^3+27*n^4)/8: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%o (Sage) [(8+6*n+81*n^2-18*n^3+27*n^4)/8 for n in (0..40)] # _G. C. Greubel_, May 26 2021
%Y Cf. A013610, A081583.
%K easy,nonn,changed
%O 0,2
%A _Paul Barry_, Mar 23 2003