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%I #22 Mar 10 2024 00:23:59
%S 0,0,1,3,7,17,40,90,198,430,922,1956,4115,8597,17853,36883,75856,
%T 155396,317228,645580,1310132,2652072,5356277,10795351,21716195,
%U 43608549,87429944,175025918,349901074,698604058,1393149486,2775103948,5522129511,10977608425
%N a(n) = Sum_{m=0..n} Sum_{i=0..m} i*C(m-i,i)*C(m-i,n-m-i).
%H Colin Barker, <a href="/A298371/b298371.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-1,-4,-3,-2,-1).
%F G.f.: x^3*(1 + x) / (1 - x - x^2 - x^3 - x^4)^2.
%F a(n) = 2*a(n-1) + a(n-2) - a(n-4) - 4*a(n-5) - 3*a(n-6) - 2*a(n-7) - a(n-8) for n>7. - _Colin Barker_, Jan 18 2018
%o (Maxima)
%o a(n):=sum(sum(i*binomial(m-i,i)*binomial(m-i,n-m-i),i,0,m),m,0,n);
%o (PARI) concat(vector(2), Vec(x^2*(1 + x) / (1 - x - x^2 - x^3 - x^4)^2 + O(x^40))) \\ _Colin Barker_, Jan 18 2018
%Y Cf. A000078.
%K nonn,easy
%O 0,4
%A _Vladimir Kruchinin_, Jan 17 2018
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