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%I #8 Nov 17 2022 19:08:00
%S 1,14,67,190,413,766,1279,1982,2905,4078,5531,7294,9397,11870,14743,
%T 18046,21809,26062,30835,36158,42061,48574,55727,63550,72073,81326,
%U 91339,102142,113765,126238,139591
%N Fifth diagonal of triangle A064094.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 1+3*n+5*n^2+5*n^3. Fourth row polynomial (n=3) of Catalan triangle A009766.
%F G.f.: (1+2*x)*(1+8*x+x^2)/(1-x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Nov 17 2022
%t CoefficientList[Series[(1 + 2*x)*(1 + 8*x + x^2)/(1 - x)^4, {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Nov 17 2022 *)
%Y Cf. A001844 (fourth diagonal), A009766, A064094.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 13 2001
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