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T(2n-1,n), where T is the array defined in A025564.
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%I #10 Sep 13 2019 22:10:37

%S 1,4,22,120,665,3732,21153,120835,694590,4013088,23284424,135580865,

%T 791862354,4637009300,27215510265,160053426720,942939231825,

%U 5564024727096,32878367902380,194530139772844,1152303896900338,6832908809693304,40556775927067299,240938382783554100

%N T(2n-1,n), where T is the array defined in A025564.

%o (PARI) T(n, k) = if( k<0 || k>2*n, 0, if(n==0, 1, polcoeff( (1 + x + x^2)^n, k)+ polcoeff( (1 + x + x^2)^(n-1), k-1)));

%o a(n) = T(2*n, n+1); \\ _Michel Marcus_, Sep 08 2019

%Y Cf. A025564.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E a(19) corrected and more terms from _Sean A. Irvine_, Sep 07 2019