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%I #18 Feb 19 2024 03:11:02
%S 1,9,44,160,491,1355,3486,8546,20245,46773,106048,236980,523535,
%T 1145935,2489202,5372534,11532633,24639513,52426420,111146280,
%U 234877811,494924179,1040183174,2181033290,4563397341,9529452605
%N Antidiagonal sums of the convolution array A213753.
%H Clark Kimberling, <a href="/A213755/b213755.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,44,-41,20,-4).
%F a(n) = (1/6)*(84 - 21*2^(n+2) + 23*n + 9*n*2^(n+2) - 3*n^2 - 2*n^3).
%F a(n) = 8*a(n-1) - 26*a(n-2) + 44*a(n-3) - 41*a(n-4) + 20*a(n-5) - 4*a(n-6).
%F G.f.: f(x)/g(x), where f(x) = x*(1 + x - 2*x^2 - 2*x^3) and g(x) = (1 - x)^4 * (1 - 2*x)^2.
%t (See A213753.)
%Y Cf. A213753, A213500.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 20 2012