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Antidiagonal sums of the convolution array A213844.
3

%I #15 Jun 17 2017 03:06:27

%S 3,23,90,250,565,1113,1988,3300,5175,7755,11198,15678,21385,28525,

%T 37320,48008,60843,76095,94050,115010,139293,167233,199180,235500,

%U 276575,322803,374598,432390,496625,567765

%N Antidiagonal sums of the convolution array A213844.

%H Clark Kimberling, <a href="/A213846/b213846.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 (5,-10,10,-5,1).

%F a(n) = n*(1 + n)*(1 - 2*n + 4*n^2)/6.

%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*(3 + 8*x + 5*x^2) and g(x) = (1-x)^5.

%t (See A213846.)

%Y Cf. A213846.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 05 2012