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A372124
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G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 9*x)^(1/3) * A(x) ).
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1
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1, 1, 5, 8, 86, 12, 2418, -6015, 97271, -490693, 4991069, -33481184, 294850612, -2232642956, 18815166552, -150373925928, 1255171140378, -10300278908424, 86135158514634, -717384480699522, 6029697856319760, -50699911500290454, 428507430151063548
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: A(x) = 2/(1 + sqrt(1-4*x*(1+9*x)^(1/3))).
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(2*k,k) * binomial(k/3,n-k)/(k+1).
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+9*x)^(1/3))))
(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(2*k, k)*binomial(k/3, n-k)/(k+1));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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