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%I #11 Apr 22 2024 12:31:04
%S 1,0,1,5,18,66,246,924,3493,13277,50697,194327,747319,2882061,
%T 11142027,43167573,167561586,651513594,2537041938,9892847952,
%U 38623197264,150959213886,590626854072,2312979822738,9065733950526,35561306875380,139595183125750
%N a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-2,n-3*k).
%F a(n) = [x^n] 1/((1-x^3) * (1-x)^(n-1)).
%F D-finite with recurrence 9*n*a(n) +3*(-17*n+16)*a(n-1) +3*(21*n-50)*a(n-2) +(-17*n+16)*a(n-3) +10*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Apr 22 2024
%p A371871 := proc(n)
%p 1/(1-x^3)/(1-x)^(n-1) ;
%p coeftayl(%,x=0,n) ;
%p end proc:
%p seq(A371871(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k-2, n-3*k));
%Y Cf. A360150, A371872, A371873.
%Y Cf. A105872, A371758.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 10 2024