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%I #16 Feb 18 2024 07:58:37
%S 1,3,10,20,42,70,120,180,275,385,546,728,980,1260,1632,2040,2565,3135,
%T 3850,4620,5566,6578,7800,9100,10647,12285,14210,16240,18600,21080,
%U 23936,26928,30345,33915,37962,42180,46930
%N Antidiagonal sums of the convolution array A213849.
%H Clark Kimberling, <a href="/A213850/b213850.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F a(n) = (n + 1)*(n + 2)*(3 - 3*(-1)^n + 8*n + 2*n^2)/96.
%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) = x*(1 + x + 2*x^2) and g(x) = (1+x)^3*(1-x)^5.
%t (See A213849.)
%Y Cf. A213849.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 05 2012
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