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A372136
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2*(1 + 9*x*A(x))^(1/3) ).
2
1, 1, 6, 24, 199, 1023, 9363, 53724, 514422, 3147234, 30860724, 197222004, 1959430572, 12936907792, 129445924524, 877093068720, 8806256385699, 60967636162677, 612785441368254, 4321431024295452, 43413113117835945, 311142782601086949, 3120889714454477613
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+2*k,k) * binomial(k/3,n-k)/(n+k+1).
PROG
(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+2*k, k)*binomial(k/3, n-k)/(n+k+1));
CROSSREFS
Sequence in context: A336267 A018981 A052594 * A320944 A277985 A091097
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 20 2024
STATUS
approved