A155084 - OEIS

A155084

A Catalan transform of [x^n](1/(1-2x-2x^2)) (A002605).

1, 2, 8, 32, 132, 552, 2328, 9872, 42020, 179336, 766888, 3284272, 14081224, 60426576, 259490736, 1114965792, 4792924356, 20611174920, 88662405768, 381494338032, 1641837542232, 7067257125744, 30425523536592

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Hankel transform is 4^n.

LINKS

Table of n, a(n) for n=0..22.

Paul Barry and Aoife Hennessy, Generalized Narayana Polynomials, Riordan Arrays, and Lattice Paths, Journal of Integer Sequences, Vol. 15, 2012, #12.4.8. [N. J. A. Sloane, Oct 08 2012]

FORMULA

G.f.: 1/(1-2x*c(x)-2(x*c(x))^2), where c(x) is the g.f. of A000108.

G.f.: 1/(1-2x-4x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction).

a(n) = Sum_{k=0..n} (k/(2n-k))*binomial(2n-k, n-k)*A002605(k), a(0) = 1.

a(n) = Sum_{0<=k<=n} A039599(n,k)*A108411(k). [Philippe Deléham, Nov 15 2009]

Apparently 3*n*a(n) +6*(3-4*n)*a(n-1) +4*(11*n-18)*a(n-2) +8*(2*n-3)*a(n-3)=0. - R. J. Mathar, Oct 25 2012

CROSSREFS

Cf. A000108, A002605, A101850, A039599, A108411.

Sequence in context: A183895 A228921 A150829 * A322251 A150830 A150831

Adjacent sequences: A155081 A155082 A155083 * A155085 A155086 A155087

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 19 2009

STATUS

approved