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 A097189 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. 1
 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; text; internal format)
 OFFSET 0,2 LINKS 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. - Vladimir Kruchinin, May 31 2011 Conjecture: n*(n-1)*a(n) - (19*n-18)*(n-1)*a(n-1) + 9*(11*n^2-31*n+22)*a(n-2) - 9*(3*n-4)*(3*n-5)*a(n-3) = 0. - R. J. Mathar, Nov 16 2012 a(n) ~ 3^(2*n+1) / (2 * GAMMA(2/3) * n^(1/3)) * (1 - sqrt(3)*GAMMA(2/3)^2 / (4*Pi*n^(1/3))). - Vaclav Kotesovec, Feb 04 2014 MATHEMATICA CoefficientList[Series[3/((1-9*x) + 2*(1-9*x)^(2/3)), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *) 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; /* Vladimir Kruchinin, May 31 2011 */ CROSSREFS Cf. A097186, A057083, A004988, A097188. Sequence in context: A070997 A122372 A083068 * A049028 A224274 A096951 Adjacent sequences:  A097186 A097187 A097188 * A097190 A097191 A097192 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 03 2004 STATUS approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)