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%I #22 Sep 08 2022 08:46:02
%S 2,34,132,332,670,1182,1904,2872,4122,5690,7612,9924,12662,15862,
%T 19560,23792,28594,34002,40052,46780,54222,62414,71392,81192,91850,
%U 103402,115884,129332,143782,159270,175832,193504,212322,232322,253540,276012,299774
%N Principal diagonal of the convolution array A213825.
%H Clark Kimberling, <a href="/A213826/b213826.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = -n - 3*n^2 + 6*n*3.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 13*x + 4*x^2) and g(x) = (1-x)^4.
%F a(n) = 2*A024215(n).
%F E.g.f.: (2 + 32*x + 33*x^2 + 6*x^3)*exp(x). - _Franck Maminirina Ramaharo_, Nov 23 2018
%t (See A213825.)
%t CoefficientList[Series[2 (1 + 13 x + 4 x^2) / (1 - x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 23 2018 *)
%o (Magma) [6*n^3-3*n^2-n: n in [1..40]]; // _Vincenzo Librandi_, Nov 23 2018
%Y Cf. A213825.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jul 04 2012
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