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%I #21 Feb 19 2024 04:07:08
%S 1,14,65,214,597,1518,3649,8462,19157,42646,93777,204294,441781,
%T 949598,2030849,4324510,9174069,19397574,40893265,85981910,180353621,
%U 377485774,788527425,1644165294,3422550037,7113537398,14763947729
%N Principal diagonal of the convolution array A213756.
%H Clark Kimberling, <a href="/A213757/b213757.txt">Table of n, a(n) for n = 1..100</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,25,-16,4).
%F a(n) = -2 + 2^(n+1) - 6*n + n*2^(n+2) - 3*n^2.
%F a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5).
%F G.f.: f(x)/g(x), where f(x) = x*(1 + 7*x - 14*x^2) and g(x) = (1 - 2*x)^2 (1 - x)^3.
%t (See A213756.)
%Y Cf. A213756, A213500.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 20 2012