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A367027
G.f. satisfies A(x) = 1 + x*A(x)^3 - x^2*A(x)^5.
0
1, 1, 2, 4, 5, -13, -147, -816, -3534, -12650, -35420, -53040, 199056, 2391340, 14555740, 68264112, 261045693, 769660569, 1167906402, -5145668100, -61758940705, -385813067255, -1857144860445, -7266981925560, -21793022441775, -32643056947527, 161919845140752
OFFSET
0,3
FORMULA
a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-k,k) * binomial(3*n-2*k,n-2*k).
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(3*n-k, k)*binomial(3*n-2*k, n-2*k))/(2*n+1);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Nov 02 2023
STATUS
approved