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%I #15 Nov 27 2017 12:18:30
%S 1,5,85,1595,33055,723701,16429435,382643525,9082868245,218790563255,
%T 5332206228085,131194789234955,3253536973286245,81224561099580155,
%U 2039348104811147845,51455631680563483835,1303889832725451598495
%N Alternate partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
%F a(n) = sum((-1)^(n-k)*binomial(2*k,k)*binomial(3*k,k),k=0..n).
%F Recurrence: (n+2)^2*a(n+2)-(26*n^2+77*n+56)*a(n+1)-3*(9*n^2+27*n+20)*a(n)=0.
%F G.f.: F(1/3,2/3;1;27*x)/(1+x), where F(a1,a2;b1;z) is a hypergeometric series.
%F a(n) ~ 3^(3*n + 7/2) / (56*Pi*n). - _Vaclav Kotesovec_, Nov 27 2017
%t Table[Sum[(-1)^(n-k)*Binomial[2k,k]Binomial[3k,k],{k,0,n}],{n,0,16}] (* fixed by _Vaclav Kotesovec_, Nov 27 2017 *)
%o (Maxima) makelist(sum(binomial(2*k,k)*binomial(3*k,k)*(-1)^(n-k),k,0,n),n,0,16);
%Y Cf. A006480, A188441, A188946, A152297.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Apr 14 2011
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