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A366591
G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)^2*A(x)^3.
4
1, 0, 0, 1, 2, 1, 3, 12, 18, 24, 75, 180, 295, 620, 1612, 3365, 6580, 15365, 35728, 74906, 163099, 379242, 848148, 1848693, 4187193, 9583209, 21417924, 48067371, 109877922, 250010451, 564688551, 1286128272, 2944963788, 6714338592, 15313680087, 35108572386
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,n-3*k) * binomial(3*k,k)/(2*k+1).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*k, n-3*k)*binomial(3*k, k)/(2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2023
STATUS
approved