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A365609
G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).
0
1, 0, 1, 1, 4, 9, 27, 78, 231, 715, 2193, 6954, 21999, 70840, 228896, 746650, 2447757, 8072208, 26745627, 89002364, 297344960, 996865397, 3352918429, 11310307593, 38256171642, 129718262583, 440855654827, 1501451066767, 5123671576890, 17516503865294
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(k,n-2*k) * binomial(n+2*k+1,k) / (n+2*k+1).
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(k, n-2*k)*binomial(n+2*k+1, k)/(n+2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 17 2023
STATUS
approved