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A349818
Central column (ignoring the zeros) of A349815, or leading entries in rows of A349816.
3
1, 1, 1, 2, 8, 13, 74, 124, 784, 1364, 9069, 16194, 111144, 202070, 1418196, 2612376, 18642208, 34682348, 250706548, 470066728, 3433030048, 6477333149, 47703926354, 90472092748, 670963514192, 1278016171132, 9534032792470, 18226719157820, 136658371126320
OFFSET
0,4
COMMENTS
Note that the analogous sequence for A349812 is the Motzkin numbers A001006.
LINKS
FORMULA
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 24 2021
EXTENSIONS
Offset corrected and terms a(21) and beyond from Andrew Howroyd, Feb 28 2023
STATUS
approved