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A115204
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Seventh column of triangle A115193 (called C(1,2)).
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4
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1, 13, 123, 1037, 8291, 64509, 494595, 3761661, 28486659, 215277565, 1625688067, 12277764093, 92783468547, 701828038653, 5314762113027, 40297495658493, 305941006516227, 2325794003091453, 17704219384479747
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OFFSET
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0,2
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COMMENTS
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Also sixth diagonal of triangle A115195, called Y(1,2), divided by 32.
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LINKS
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FORMULA
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G.f.: (-1 + 7*x - 8*x^2 + (1- 9*x + 18*x^2 - 4*x^3)*c(2*x))/(16*(1+x)*x^5), with the o.g.f. c(x) of A000108 (Catalan).
G.f. is also: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^6)/(64*(1+x)*x^6).
a(n) = (-1)^n*2^(8+3*n)*(Binomial[1/2, 4 + n]*Hypergeometric2F1[1, 7/2 + n, 5 + n, -8] + 4*(9*Binomial[1/2, 5 + n]*Hypergeometric2F1[1, 9/2 + n, 6 + n, -8] + 36*Binomial[1/2, 6 + n]*Hypergeometric2F1[1, 11/2 + n, 7 + n, -8] + 32*Binomial[1/2, 7 + n]*Hypergeometric2F1[1, 13/2 + n, 8 + n, -8])). - G. C. Greubel, Feb 04 2016
D-finite with recurrence 2*n*(n+6)*a(n) +(-11*n^2-51*n-120)*a(n-1) +(-37*n^2-99*n-132)*a(n-2) -12*(n+1)*(2*n+1)*a(n-3)=0. - R. J. Mathar, Mar 10 2022
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MATHEMATICA
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f[n_] := SeriesCoefficient[(1 - 13*x + 46*x^2 - 36*x^3 -(1 - 9*x + 18*x^2 - 4*x^3) Sqrt[1 - 8*x])/(64*x^6*(1 + x)), {x, 0, n}];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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