A130524 Diagonal immediately below the main diagonal of square array A130523.

1, 4, 18, 87, 442, 2332, 12677, 70605, 401172, 2317683, 13578615, 80502845, 482140580, 2912954090, 17733363776, 108674957854, 669843377831, 4148242390236, 25757224787638, 159544222448006, 974349264795556

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 * A298646 A199309 A083325

Adjacent sequences: A130521 A130522 A130523 * A130525 A130526 A130527

Keyword

nonn

Author

Paul D. Hanna, Jun 02 2007

Status

approved