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%I #17 Jun 17 2017 02:59:44
%S 3,32,119,296,595,1048,1687,2544,3651,5040,6743,8792,11219,14056,
%T 17335,21088,25347,30144,35511,41480,48083,55352,63319,72016,81475,
%U 91728,102807,114744,127571,141320,156023,171712
%N Principal diagonal of the convolution array A213844.
%H Clark Kimberling, <a href="/A213845/b213845.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (2*n - 9*n^2 + 16*n^3)/3.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: f(x)/g(x), where f(x) = x*(3 + 20*x + 9*x^2) and g(x) = (1-x)^4.
%t (See A213841.)
%t LinearRecurrence[{4,-6,4,-1},{3,32,119,296},40] (* _Harvey P. Dale_, Nov 06 2014 *)
%Y Cf. A213841.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jul 05 2012