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A367073
G.f. satisfies A(x) = 1 + 2*x + x^3*A(x)^3.
3
1, 2, 0, 1, 6, 12, 11, 30, 120, 252, 408, 1104, 3415, 7710, 15984, 42609, 118422, 281820, 657468, 1732008, 4608288, 11375240, 28100400, 73598112, 192776895, 487507038, 1239516384, 3241480275, 8460205842, 21733941060, 56121723411, 146904032622, 383900676120
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+1,n-3*k) * A001764(k).
PROG
(PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+1, n-3*k)*binomial(3*k, k)/(2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 05 2023
STATUS
approved