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%I #21 Sep 22 2017 04:44:26
%S 1,10,56,240,880,2912,8960,26112,72960,197120,518144,1331200,3354624,
%T 8314880,20316160,49020928,116981760,276430848,647495680,1504706560,
%U 3471835136,7958691840,18136170496,41104179200,92694118400,208071032832,465064427520
%N Expansion of (1+2*x) / (1-2*x)^4.
%H Colin Barker, <a href="/A014483/b014483.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 (8,-24,32,-16).
%F a(n) = 2^n * A000330(n+1). - _R. J. Mathar_, Oct 23 2008
%F From _Colin Barker_, Feb 13 2017: (Start)
%F a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>3.
%F a(n) = (2^(n-1)*(6 + 13*n + 9*n^2 + 2*n^3)) / 3. (End)
%F a(n) = (1/2) * Sum_{k=0..n+1} Sum_{i=0..n+1} (n-i+1)^2 * C(n+1,k). - _Wesley Ivan Hurt_, Sep 21 2017
%o (PARI) Vec((1 + 2*x) / (1 - 2*x)^4 + O(x^30)) \\ _Charles R Greathouse IV_, Sep 26 2012, corrected by _Colin Barker_, Feb 13 2017
%Y Cf. A087076, A058645.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Feb 13 2017
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