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A097189
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Row sums of triangle A097186, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A057083(y)^(n+1), where R_n(1/3) = 3^n for all n>=0.
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1
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1, 7, 55, 451, 3781, 32131, 275563, 2378971, 20640907, 179791327, 1571002291, 13762897435, 120832716655, 1062818450155, 9363143224315, 82600459304203, 729572125425661, 6450872644562491, 57092964352312951, 505729048454449651
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: A(x) = 3/((1-9*x) + 2*(1-9*x)^(2/3)). G.f.: A(x) = A004988(x)/(1 - x*A097188(x)).
a(n)=sum(m=1..n-1, sum(k=1..n-m, binomial(k,n-m-k)*(-3)^(k)*binomial(k+n-1,n-1)))+1; [From Vladimir Kruchinin, May 31 2011]
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PROG
| (PARI) a(n)=polcoeff(3/((1-9*x)+2*(1-9*x+x*O(x^n))^(2/3)), n, x)
(Maxima)
a(n):=sum(sum(binomial(k, n-m-k)*(-3)^(k)*binomial(k+n-1, n-1), k, 1, n-m), m, 1, n-1)+1; [From Vladimir Kruchinin, May 31 2011]
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CROSSREFS
| Cf. A097186, A057083, A004988, A097188.
Sequence in context: A070997 A122372 A083068 * A049028 A096951 A113714
Adjacent sequences: A097186 A097187 A097188 * A097190 A097191 A097192
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 03 2004
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