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%I #24 Feb 14 2018 16:31:05
%S 0,8,38,102,212,380,618,938,1352,1872,2510,3278,4188,5252,6482,7890,
%T 9488,11288,13302,15542,18020,20748,23738,27002,30552,34400,38558,
%U 43038,47852,53012,58530,64418,70688,77352,84422,91910,99828,108188,117002
%N a(n) = n*(2*n^2 + 5*n + 1).
%C Row sums of triangle A155156.
%H Vincenzo Librandi, <a href="/A163832/b163832.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: -2*x*(1+x)*(x-4)/(x-1)^4.
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
%F a(n) = A163683(n) + n = A163815(n) - 2*n = 2*A162254(n).
%F a(n) = -n*A168244(n+2). - _Bruno Berselli_, Feb 02 2012
%F E.g.f.: x*(8 + 11*x + 2*x^2)*exp(x). - _G. C. Greubel_, Aug 05 2017
%t Table[n(2n^2+5n+1),{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,8,38,102},40] (* _Harvey P. Dale_, Feb 02 2012 *)
%o (PARI) for(n=0, 40, print1(n*(2*n^2+5*n+1)", ")); \\ _Vincenzo Librandi_, Feb 22 2012
%Y Cf. A155156.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Aug 05 2009
%E Edited by _R. J. Mathar_, Aug 05 2009
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