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%I #21 Aug 29 2023 05:09:51
%S 1,1,2,5,15,47,153,514,1769,6205,22102,79733,290721,1069688,3966739,
%T 14810348,55627778,210046102,796864028,3035912900,11610468138,
%U 44556451207,171529074168,662238211929,2563524741603,9947573055828,38687704042595
%N G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).
%F D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +(-2*n+7)*a(n-5) +(n-8)*a(n-6) +(n-8)*a(n-8)=0. - _R. J. Mathar_, Aug 29 2023
%p A364161 := proc(n)
%p add( binomial(n-2*k-1,k)*binomial(2*n-5*k+1,n-3*k)/(2*n5*k+1),k=0..floor(n/3)) ;
%p end proc:
%p seq(A364161(n),n=0..80); # _R. J. Mathar_, Aug 29 2023
%o (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));
%Y Cf. A001003, A119370.
%Y Cf. A218251, A364833, A365247.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 28 2023
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