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A287702 a(n) = (3!)^3 * [z^3] hypergeom([], [1,1], z)^n.

%I A287702 #11 Aug 20 2017 14:53:33
%S A287702 0,1,56,381,1192,2705,5136,8701,13616,20097,28360,38621,51096,66001,
%T A287702 83552,103965,127456,154241,184536,218557,256520,298641,345136,396221,
%U A287702 452112,513025,579176,650781,728056,811217,900480,996061,1098176,1207041,1322872,1445885
%N A287702 a(n) = (3!)^3 * [z^3] hypergeom([], [1,1], z)^n.
%H A287702 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A287702 O.g.f.: x*(1 + 52*x + 163*x^2) / (1 - x)^4.
%F A287702 a(n) = 46*n - 81*n^2 + 36*n^3.
%F A287702 a(n) = [x^n] (x + 52*x^2 + 163*x^3) / (1 - x)^4.
%p A287702 a := n -> 46*n - 81*n^2 + 36*n^3: seq(a(n), n=0..35);
%t A287702 Table[46 n - 81 n^2 + 36 n^3, {n, 0, 40}] (* _Bruno Berselli_, Jun 06 2017 *)
%t A287702 LinearRecurrence[{4,-6,4,-1},{0,1,56,381},40] (* _Harvey P. Dale_, Aug 20 2017 *)
%Y A287702 Column 3 of A287698.
%K A287702 nonn,easy
%O A287702 0,3
%A A287702 _Peter Luschny_, Jun 01 2017