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%I #27 Sep 04 2019 02:24:26
%S 1,4,23,141,888,5676,36622,237821,1551727,10161409,66732392,439267525,
%T 2897064773,19137833146,126599140313,838477244705,5559158604616,
%U 36891869005316,245025744759152,1628602268643928,10832010390274304,72088640151558145,480026332241373281,3198037386794785777,21315944308822771118
%N T(3*n + 1, n + 1), array T as in A038792.
%F G.f.: (g-1)^2/((1-3*g)*(g^2-3*g+1)) where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 10 2011
%F a(n) = A134511(4n,2n). - _Alois P. Heinz_, Mar 02 2018
%F a(n) = Sum_{j=0..n} binomial(4*n-j, j). - _Petros Hadjicostas_, Sep 04 2019
%F a(n) = hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)* hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4) for n > 0. - _Peter Luschny_, Sep 04 2019
%F a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n-1)). - _Vaclav Kotesovec_, Sep 04 2019
%p a := n -> `if`(n=0, 1, hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)*hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4)):
%p seq(simplify(a(n)), n = 0..24); # _Peter Luschny_, Sep 04 2019
%Y Cf. A038792, A134511.
%K nonn
%O 0,2
%A _Clark Kimberling_, May 02 2000
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