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Search: id:A130524
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| A130524 |
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Diagonal immediately below the main diagonal of square array A130523. |
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+0
3
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| 1, 4, 18, 87, 442, 2332, 12677, 70605, 401172, 2317683, 13578615, 80502845, 482140580, 2912954090, 17733363776, 108674957854, 669843377831, 4148242390236, 25757224787638, 159544222448006, 974349264795556
(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) = C(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(C*D*F+x*O(x^n), n, x)}
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CROSSREFS
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Cf. A130523; diagonals: A007857, A130525; related: A000108, A001764.
Sequence in context: A084847 A082685 A111966 this_sequence A083325 A050146 A083879
Adjacent sequences: A130521 A130522 A130523 this_sequence A130525 A130526 A130527
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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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