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A130525 Diagonal immediately above the main diagonal of square array A130523. 2
1, 3, 13, 63, 324, 1733, 9541, 53725, 308085, 1793528, 10574165, 63018105, 379061652, 2298508872, 14035737150, 86239762294, 532743452260, 3305228985864, 20546951820588, 127237301998014, 774257153670067 (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) = 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 * A243280 A000259 A007855

Adjacent sequences:  A130522 A130523 A130524 * A130526 A130527 A130528

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 02 2007

STATUS

approved

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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)