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A365691
G.f. satisfies A(x) = 1 + x^2*A(x)^5 / (1 - x*A(x)).
2
1, 0, 1, 1, 6, 12, 54, 147, 593, 1886, 7292, 25204, 96153, 348304, 1327716, 4946471, 18936366, 71827598, 276612103, 1062220253, 4115807184, 15947902376, 62148513732, 242485933208, 949828266722, 3726623622402, 14663689944397, 57798199213989
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,n-2*k) * binomial(n+3*k+1,k) / (n+3*k+1).
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, n-2*k)*binomial(n+3*k+1, k)/(n+3*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2023
STATUS
approved