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Central column (ignoring the zeros) of A349815, or leading entries in rows of A349816.
3

%I #10 Feb 28 2023 17:04:16

%S 1,1,1,2,8,13,74,124,784,1364,9069,16194,111144,202070,1418196,

%T 2612376,18642208,34682348,250706548,470066728,3433030048,6477333149,

%U 47703926354,90472092748,670963514192,1278016171132,9534032792470,18226719157820,136658371126320

%N Central column (ignoring the zeros) of A349815, or leading entries in rows of A349816.

%C Note that the analogous sequence for A349812 is the Motzkin numbers A001006.

%H Andrew Howroyd, <a href="/A349818/b349818.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = [x^floor(3*n/2+1)](-1 - x + x^2 + 3*x^3)*(1 + x + x^2 + x^3)^(n-1) for n > 0. - _Andrew Howroyd_, Feb 28 2023

%o (PARI) a(n) = if(n==0, 1, polcoef((-1 - x + x^2 + x^3)*(1 + x + x^2 + x^3)^(n-1), 3*n\2+1)) \\ _Andrew Howroyd_, Feb 28 2023

%Y Cf. A001006, A349812, A349815, A349816.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Dec 24 2021

%E Offset corrected and terms a(21) and beyond from _Andrew Howroyd_, Feb 28 2023