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A371522
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.
5
1, 3, 24, 235, 2586, 30603, 380359, 4896753, 64731747, 873539236, 11984536632, 166661420814, 2343950447112, 33282048811530, 476462982915993, 6869620848003570, 99663539644072305, 1453861111238442363, 21312207036239313936, 313783619269186619589
OFFSET
0,2
FORMULA
a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+2,k)/(5*k+3).
G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349333.
PROG
(PARI) a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2024
STATUS
approved