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%I #10 Apr 22 2019 10:24:50
%S 1,4,20,68,175,392,786,1440,2475,4036,6292,9464,13805,19600,27200,
%T 36996,49419,64980,84238,107800,136367,170696,211600,260000,316881,
%U 383292,460404,549460,651775,768800,902066,1053184,1223915,1416108,1631700,1872792,2141581
%N Column 3 of triangle A123610.
%H G. C. Greubel, <a href="/A123613/b123613.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,6,-9,12,-9,6,-6,4,-1).
%F G.f.: P_3(x) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2), with P_3(1) = 5!, where P_3(x) = (1+2*x+11*x^2+26*x^3+30*x^4+26*x^5+17*x^6+6*x^7+x^8).
%t CoefficientList[Series[(1 + 2*x + 11*x^2 + 26*x^3 + 30*x^4 + 26*x^5 + 17*x^6 + 6*x^7 + x^8)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 16 2017 *)
%t LinearRecurrence[{4,-6,6,-9,12,-9,6,-6,4,-1},{1,4,20,68,175,392,786,1440,2475,4036},40] (* _Harvey P. Dale_, Apr 22 2019 *)
%o (PARI) {a(n)=polcoeff(truncate(Ser([1,2,11,26,30,26,17,6,1]))/((1-x)^2*(1-x^2)^2*(1-x^3)^2 +x*O(x^n)),n)}
%Y Cf. A123610 (triangle); columns: A005997, A123614, A123615, A123616.
%K nonn,easy
%O 0,2
%A _Paul D. Hanna_, Oct 03 2006
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