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%I #12 Jan 14 2023 08:46:01
%S 1,6,35,252,1716,12870,92378,705432,5200300,40116600,300540195,
%T 2333606220,17672631900,137846528820,1052049481860,8233430727600,
%U 63205303218876,495918532948104,3824345300380220,30067266499541040,232714176627630544,1832624140942590534,14226520737620288370,112186277816662845432,873065282167813104916
%N A trisection of A001405 (central binomial coefficients): binomial(3n+1,floor((3n+1)/2)), n>=0.
%C For trisection of sequences see a comment and a reference under A187357.
%F a(n) = binomial(3*n+1,floor((3*n+1)/2)), n>=0.
%F O.g.f.: 3!*x*G2(x^2) + G1(x^2), with G2(x) and G1(x) the o.g.f.s of A187365 and A187364, respectively.
%t Table[Binomial[3n+1,Floor[(3n+1)/2]],{n,0,30}] (* _Harvey P. Dale_, Jan 13 2021 *)
%Y Cf. A187442: binomial(3n,floor(3n/2)), A187444: binomial(3n+2,floor((3n+2)/2))/2.
%Y Cf. A187357, A187364, A187365.
%Y Cf. A001405.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Mar 10 2011
%E Corrected and extended by _Harvey P. Dale_, Jan 13 2021
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