

A155084


A Catalan transform of [x^n](1/(12x2x^2)) (A002605).


1



1, 2, 8, 32, 132, 552, 2328, 9872, 42020, 179336, 766888, 3284272, 14081224, 60426576, 259490736, 1114965792, 4792924356, 20611174920, 88662405768, 381494338032, 1641837542232, 7067257125744, 30425523536592
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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/(12x*c(x)2(x*c(x))^2), where c(x) is the g.f. of A000108.
G.f.: 1/(12x4x^2/(12xx^2/(12xx^2/(12xx^2/(1..... (continued fraction).
a(n) = Sum_{k=0..n} (k/(2nk))*binomial(2nk, nk)*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*(34*n)*a(n1) +4*(11*n18)*a(n2) +8*(2*n3)*a(n3)=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



