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%I #20 Sep 08 2022 08:45:25
%S 4,40,240,1088,4160,14208,44800,133120,377856,1034240,2748416,7127040,
%T 18104320,45187072,111083520,269484032,646184960,1533542400,
%U 3606052864,8409579520,19465764864,44753223680,102257131520,232330887168
%N a(n) = n*(1 + n^2)*2^n.
%H Vincenzo Librandi, <a href="/A119635/b119635.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 (8,-24,32,-16).
%F G.f.: 4*x*(1 + 2*x + 4*x^2)/(1 - 2*x)^4. - _Vincenzo Librandi_, Feb 22 2013
%F E.g.f.: 4*x*(1 + 3*x + 2*x^2)*exp(2*x). - _G. C. Greubel_, Mar 04 2019
%p [(n^3+n)*2^n$n=1..30]; # _Muniru A Asiru_, Mar 04 2019
%t Table[(n^3 + n)*2^n, {n, 30}] (* or *) CoefficientList[Series[4(1 +2x + 4x^2)/(1-2x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 22 2013 *)
%o (Magma) [(n^3 + n)*2^n: n in [1..30]]; // _Vincenzo Librandi_, Feb 22 2013
%o (GAP) List([1..30],n->n*(n^2+1)*2^n); # _Muniru A Asiru_, Mar 04 2019
%o (PARI) {a(n) = n*(1+n^2)*2^n}; \\ _G. C. Greubel_, Mar 04 2019
%o (Sage) [n*(1+n^2)*2^n for n in (1..30)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A128796, A128960, A128985, A129002.
%K nonn,easy
%O 1,1
%A _Mohammad K. Azarian_, May 02 2007
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