A130525 Diagonal immediately above the main diagonal of square array A130523.

1, 3, 13, 63, 324, 1733, 9541, 53725, 308085, 1793528, 10574165, 63018105, 379061652, 2298508872, 14035737150, 86239762294, 532743452260, 3305228985864, 20546951820588, 127237301998014, 774257153670067

Offset

0,2

Links

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

Formula

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).

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(D*F+x*O(x^n), n, x)}

Crossrefs

Cf. A130523; diagonals: A007857, A130524; related: A000108, A001764.

Sequence in context: A034478 A026715 A001850 * A362744 A350519 A243280

Adjacent sequences: A130522 A130523 A130524 * A130526 A130527 A130528

Keyword

nonn

Author

Paul D. Hanna, Jun 02 2007

Status

approved