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%I #14 Feb 08 2022 19:57:35
%S 1,4,11,25,51,96,169,281,445,676,991,1409,1951,2640,3501,4561,5849,
%T 7396,9235,11401,13931,16864,20241,24105,28501,33476,39079,45361,
%U 52375,60176,68821,78369,88881,100420,113051,126841,141859,158176,175865,195001
%N Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0, ...].
%H Alois P. Heinz, <a href="/A136395/b136395.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 A007318 * [1, 3, 4, 3, 2, 0, 0, 0, ...]. A001263 * [1, 3, 1, 0, 0, 0, ...]
%F O.g.f.: -(1-x+x^2+x^4)/(-1+x)^5. - _R. J. Mathar_, Apr 02 2008
%e a(3) = 25 = (1, 3, 3, 1) dot (1, 3, 4, 3) = (1 + 9 + 12 + 3).
%e a(3) = 25 = (1, 6, 6, 1) dot (1, 3, 1, 0) = (1 + 18 + 6 + 0), where (1, 6, 6, 1) = row 4 of the Narayana triangle, A001263.
%p a := n-> (Matrix([[11,4,1,1,5]]). Matrix(5, (i,j)-> if (i=j-1) then 1 elif j=1 then [5,-10,10,-5,1][i] else 0 fi)^n)[1,3]; seq (a(n), n=0..50); # _Alois P. Heinz_, Aug 14 2008
%t CoefficientList[Series[-(1-x+x^2+x^4)/(-1+x)^5,{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,4,11,25,51},40] (* _Harvey P. Dale_, Dec 27 2016 *)
%Y Cf. A001263.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Dec 29 2007
%E More terms from _R. J. Mathar_, Apr 02 2008
%E More terms from _Alois P. Heinz_, Aug 14 2008
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