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A130524 Diagonal immediately below the main diagonal of square array A130523. 3
1, 4, 18, 87, 442, 2332, 12677, 70605, 401172, 2317683, 13578615, 80502845, 482140580, 2912954090, 17733363776, 108674957854, 669843377831, 4148242390236, 25757224787638, 159544222448006, 974349264795556 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

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).

PROG

(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)}

CROSSREFS

Cf. A130523; diagonals: A007857, A130525; related: A000108, A001764.

Sequence in context: A153294 A164045 A178577 * A199309 A083325 A050146

Adjacent sequences:  A130521 A130522 A130523 * A130525 A130526 A130527

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 02 2007

STATUS

approved

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Last modified July 29 08:51 EDT 2014. Contains 245020 sequences.