A090413 A Chebyshev transform of 3^n.

1, 3, 8, 21, 56, 150, 400, 1065, 2840, 7578, 20208, 53874, 143664, 383148, 1021728, 2724465, 7265240, 19374450, 51665200, 137772246, 367392656, 979719348, 2612584928, 6966873546, 18578329456, 49542281220, 132112749920

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

G.f.: c(-x^2)/(1-3xc(-x^2)), c(x) g.f. of Catalan numbers A000108; a(n)=sum{k=0..n, (k+1)C(n, n/2-k/2)(-1)^(n/2-k/2)(1+(-1)^(n+k))3^k/(n+k+2)}.

Conjecture: 3*(n+1)*a(n) -8*(n+1)*a(n-1) +12*(n-2)*a(n-2) +32*(2-n)*a(n-3)=0. - R. J. Mathar, Sep 27 2012

Crossrefs

Sequence in context: A309226 A278616 A278615 * A128105 A085560 A318900

Adjacent sequences: A090410 A090411 A090412 * A090414 A090415 A090416

Keyword

easy,nonn

Author

Paul Barry, Dec 05 2003

Status

approved