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%I #18 Sep 08 2022 08:46:19
%S 0,1,346,6219,36628,124405,316206,672511,1267624,2189673,3540610,
%T 5436211,8006076,11393629,15756118,21264615,28104016,36473041,
%U 46584234,58663963,72952420,89703621,109185406,131679439,157481208,186900025,220259026,257895171,300159244
%N a(n) = (4!)^3 * [z^4] hypergeom([], [1,1], z)^n.
%H Vincenzo Librandi, <a href="/A287700/b287700.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F O.g.f.: x*(1 + 341*x + 4499*x^2 + 8983*x^3)/(1 - x)^5.
%F a(n) = -1899*n + 3916*n^2 - 2592*n^3 + 576*n^4.
%F a(n) = [x^n] (x + 341*x^2 + 4499*x^3 + 8983*x^4) / (1 - x)^5.
%p a := n -> -1899*n + 3916*n^2 - 2592*n^3 + 576*n^4: seq(a(n), n=0..27);
%t Table[-1899 n + 3916 n^2 - 2592 n^3 + 576 n^4, {n, 0, 30}] (* _Bruno Berselli_, Jun 06 2017 *)
%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 346, 6219, 36628}, 30] (* _Vincenzo Librandi_, Jul 20 2017 *)
%o (Magma) [-1899*n + 3916*n^2 - 2592*n^3 + 576*n^4: n in [0..30]]; // _Vincenzo Librandi_, Jul 20 2017
%Y Column 4 of A287698.
%K nonn,easy
%O 0,3
%A _Peter Luschny_, May 31 2017
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