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Search: id:A130525
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| A130525 |
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Diagonal immediately above the main diagonal of square array A130523. |
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+0
3
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| 1, 3, 13, 63, 324, 1733, 9541, 53725, 308085, 1793528, 10574165, 63018105, 379061652, 2298508872, 14035737150, 86239762294, 532743452260, 3305228985864, 20546951820588, 127237301998014, 774257153670067
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: A(x) = D(x)*F(x), where D(x) = 1/[1 - xC(x)F(x) - xF(x)^2)] is the g.f. of the main diagonal (A007857), C(x) = 1 + xC(x)^2 is the g.f. of Catalan numbers (A000108), and F(x) = 1 + xF(x)^3 is the g.f. of ternary numbers (A001764).
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PROGRAM
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(PARI) {a(n)=local(C, F, D); C=Ser(vector(n+1, r, binomial(2*r-2, r-1)/r)); F=Ser(vector(n+1, r, binomial(3*r-3, r-1)/(2*r-1))); D=1/(1-x*C*F-x*F^2); polcoeff(D*F+x*O(x^n), n, x)}
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CROSSREFS
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Cf. A130523; diagonals: A007857, A130524; related: A000108, A001764.
Adjacent sequences: A130522 A130523 A130524 this_sequence A130526 A130527 A130528
Sequence in context: A034478 A026715 A001850 this_sequence A000259 A007855 A107097
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 02 2007
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