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Principal diagonal of the convolution array A213747.
3

%I #15 Nov 07 2017 05:26:02

%S 1,16,125,758,4071,20424,98185,458506,2096651,9436172,41941005,

%T 184545294,805298191,3489644560,15032352785,64424443922,274877775891,

%U 1168230842388,4947801800725,20890719879190,87960928124951

%N Principal diagonal of the convolution array A213747.

%H Clark Kimberling, <a href="/A213748/b213748.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 (12,-53,106,-96,32).

%F a(n) = 12*a(n-1) - 53*a(n-2) + 106*a(n-3) - 96*a(n-4) + 32*a(n-5).

%F G.f.: f(x)/g(x), where f(x) = x*(1 + 4*x - 14*x^2) and g(x) = (1 - 2*x)*(1 - 5*x + 4*x^2)^2.

%F a(n) = 2 - 2^n + 4^n*(n-1) + n. - _Colin Barker_, Nov 07 2017

%t (See A213747.)

%t LinearRecurrence[{12,-53,106,-96,32},{1,16,125,758,4071},30] (* _Harvey P. Dale_, Aug 15 2012 *)

%Y Cf. A213747, A213500.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 19 2012