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A360083
a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k).
3
1, 1, 7, 35, 189, 1092, 6538, 40278, 253730, 1626858, 10582616, 69669273, 463319257, 3107941405, 21004392887, 142882885210, 977562617826, 6722361860888, 46438235933700, 322111000796428, 2242538435656450, 15665017062799230, 109761527468995102
OFFSET
0,3
FORMULA
G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^5 * A(x)).
G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^5 )).
PROG
(PARI) a(n) = sum(k=0, n, binomial(5*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)^5)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2023
STATUS
approved