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A368935
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3) ).
2
1, 2, 7, 29, 132, 637, 3200, 16554, 87576, 471570, 2575885, 14238003, 79487023, 447540164, 2538352756, 14489355578, 83174465721, 479842193453, 2780625587824, 16178040713569, 94467163314370, 553430174678595, 3251969073086610, 19161172609833540, 113186247571818096
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+k,k) * binomial(3*n-2*k+1,n-3*k).
PROG
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n+k, k)*binomial(3*n-2*k+1, n-3*k))/(n+1);
(PARI) my(x='x+O('x^30)); Vec(serreverse(x*(1-x)*(1-x+x^3))/x) \\ Michel Marcus, Jan 10 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 10 2024
STATUS
approved