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%I #14 Feb 09 2017 12:01:49
%S 4,30,114,310,690,1344,2380,3924,6120,9130,13134,18330,24934,33180,
%T 43320,55624,70380,87894,108490,132510,160314,192280,228804,270300,
%U 317200,369954,429030,494914,568110,649140
%N Antidiagonal sums of the convolution array A213822.
%C Every term is even.
%H Clark Kimberling, <a href="/A213824/b213824.txt">Table of n, a(n) for n = 1..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 a(n) = (2*n + 5*n^2 + 6*n^3 + 3*n^4)/4 = n*(1 + n)*(2 + 3*n + 3*n^2)/4.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: f(x)/g(x), where f(x) = 2*x*(2 + 5*x + 2*x^2) and g(x) = (1-x)^5.
%F a(n) = Sum_{i=1..n} i*(3*i^2+1). - _Bruno Berselli_, Feb 09 2017
%t (See A213822.)
%o (PARI) a(n) = n*(3*n^3 + 6*n^2 + 5*n + 2)/4 \\ _Charles R Greathouse IV_, Feb 09 2017
%Y Cf. A213822.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jul 04 2012
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