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Main diagonal of the square array A058395.
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%I #11 Apr 17 2023 06:35:17

%S 1,1,4,10,25,61,146,344,800,1840,4192,9472,21248,47360,104960,231424,

%T 507904,1110016,2416640,5242880,11337728,24444928,52559872,112721920,

%U 241172480,514850816,1096810496,2332033024,4949278720,10485760000,22179479552,46841987072

%N Main diagonal of the square array A058395.

%C Binomial transform of 1, 0, 3, 0, 6, 0, 10, 0, 15, 0, ... (triangular numbers alternating with zeros).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).

%F a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 5.

%F a(n) = A158920(n+1) - A158920(n).

%F a(n) = Sum_{k=0..n} A007318(n,k)*A008805(k)*(1 + (-1)^k)/2.

%F G.f.: (1-x)^5/(1-2*x)^3.

%Y Cf. A000217, A007318, A008805, A058395, A158920.

%K nonn,easy

%O 0,3

%A _Philippe Deléham_, Apr 10 2023