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A364552
G.f. satisfies A(x) = 1 + x*A(x) + x^4*A(x)^3.
3
1, 1, 1, 1, 2, 5, 11, 21, 39, 78, 169, 373, 808, 1727, 3719, 8153, 18100, 40315, 89770, 200250, 448755, 1010685, 2284295, 5173961, 11740697, 26699780, 60863291, 139045991, 318247190, 729572315, 1675085099, 3851795549, 8869990949, 20453679944, 47223844863
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(n-k,3*k) * binomial(3*k,k) / (2*k+1).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n-k, 3*k)*binomial(3*k, k)/(2*k+1));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 28 2023
STATUS
approved