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%I #16 Oct 21 2022 21:24:43
%S 0,0,9,144,765,2475,6120,12789,23814,40770,65475,99990,146619,207909,
%T 286650,385875,508860,659124,840429,1056780,1312425,1611855,1959804,
%U 2361249,2821410,3345750,3939975,4610034,5362119,6202665,7138350,8176095,9323064,10586664
%N a(n) = (3/8)*(n-1)*(n-2)*(27*n^2-137*n+180).
%H G. C. Greubel, <a href="/A134176/b134176.txt">Table of n, a(n) for n = 1..1000</a>
%H D. Zvonkine, <a href="http://www.math.jussieu.fr/~zvonkine/">Home Page</a>
%H D. Zvonkine, <a href="http://mi.mathnet.ru/eng/mmj274">Counting ramified coverings and intersection theory on Hurwitz spaces II (local structure of Hurwitz spaces and combinatorial results)</a>, Moscow Mathematical Journal, vol. 7 (2007), no. 1, 135-162.
%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.: 9*x^3*(1+11*x+15*x^2)/(1-x)^5 . - _R. J. Mathar_, Feb 01 2008
%t Table[(3/8)(n-1)(n-2)(27n^2-137n+180),{n,40}] (* _Harvey P. Dale_, Mar 23 2011 *)
%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 9, 144, 765} , 50] (* _G. C. Greubel_, May 30 2016 *)
%o (PARI) a(n)=3*(n-1)*(n-2)*(27*n^2-137*n+180)/8 \\ _Charles R Greathouse IV_, Oct 21 2022
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Jan 30 2008