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A372036
G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)/(1 - x) )^(1/3).
1
1, 3, 3, -6, 3, 57, -141, -321, 2460, -1572, -29400, 92505, 196905, -1841208, 1608636, 24028995, -85167204, -161127519, 1756947801, -1901675715, -23476298442, 91225005105, 149447955855, -1890518796654, 2421742054233, 25239556328043, -106352841162777
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} 9^k * binomial(k/3+1/3,k) * binomial(n-1,n-k)/(k+1).
PROG
(PARI) a(n) = sum(k=0, n, 9^k*binomial(k/3+1/3, k)*binomial(n-1, n-k)/(k+1));
CROSSREFS
Cf. A372017.
Sequence in context: A086222 A278663 A086492 * A143305 A051472 A257957
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 16 2024
STATUS
approved