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A370695
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G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/4) / (1-x))^4.
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0
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1, 4, 22, 128, 777, 4872, 31330, 205560, 1370868, 9266104, 63343006, 437183260, 3042337215, 21323543252, 150395596016, 1066637271424, 7602188660799, 54422262148632, 391146728466980, 2821396586367568, 20417766975784066, 148200184917042112
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 4 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+4,k)/(3*k+4).
G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A307678.
a(n) ~ 9 * 31^(n + 1/2) / (sqrt(Pi) * n^(3/2) * 2^(2*n + 3)). - Vaclav Kotesovec, Mar 29 2024
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PROG
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(PARI) a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+4, k)/(3*k+4));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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