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

1, 4, 18, 87, 442, 2332, 12677, 70605, 401172, 2317683, 13578615, 80502845, 482140580, 2912954129, 17733375207, 108676158775, 669914021414, 4151053001800, 25841001981211, 161534820531068, 1013566626969398, 6381398103680604, 40301852983776764, 255249505209864803, 1620819715569894894

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: A(x) = C(x)*D(x)*F(x), where D(x) = 1/(1 - x*C(x)*F(x) - x*F(x)^2) is the g.f. of the main diagonal (A007857), C(x) = 1 + x*C(x)^2 is the g.f. of Catalan numbers (A000108) and F(x) = 1 + x*F(x)^3 is the g.f. of ternary numbers (A001764).

Prog

(PARI) {a(n) = my(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); polcoef(C*D*F+x*O(x^n), n, x)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

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

Sequence in context: A381889 A164045 A178577 * A298646 A385120 A199309

Adjacent sequences: A130521 A130522 A130523 * A130525 A130526 A130527

Keyword

nonn

Author

Paul D. Hanna, Jun 02 2007

Extensions

Edited and corrected by Paul D. Hanna, Jan 27 2025

Status

approved