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A360082
a(n) = Sum_{k=0..n} binomial(4*k,n-k) * Catalan(k).
5
1, 1, 6, 27, 134, 709, 3892, 22004, 127250, 749230, 4476386, 27071344, 165398868, 1019405720, 6330482488, 39571612357, 248796862550, 1572300095758, 9981970108384, 63633339713190, 407162295120570, 2614059813642256, 16834457481559076
OFFSET
0,3
FORMULA
G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^4 * A(x)).
G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^4 )).
PROG
(PARI) a(n) = sum(k=0, n, binomial(4*k, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^4)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2023
STATUS
approved