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A371518
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^2.
4
1, 2, 11, 72, 525, 4104, 33647, 285526, 2486809, 22103726, 199697284, 1828472914, 16929944932, 158246198836, 1491210732346, 14151603542612, 135130396860130, 1297381593071890, 12516650939119421, 121281286192026308, 1179769340479567499
OFFSET
0,2
FORMULA
a(n) = 2 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(4*k+1,k)/(3*k+2).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349331.
PROG
(PARI) a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+1, k)/(3*k+2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2024
STATUS
approved