|
| |
|
|
A102898
|
|
A Catalan-related transform of 3^n.
|
|
0
|
|
|
|
1, 3, 9, 30, 99, 330, 1098, 3660, 12195, 40650, 135486, 451620, 1505358, 5017860, 16726068, 55753560, 185844771, 619482570, 2064940470, 6883134900, 22943778138, 76479260460, 254930851404, 849769504680, 2832564956814
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Transform of 1/(1-3x) under the mapping g(x)->g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. The inverse transform is h(x)->h(x/(1+x^2)).
|
|
|
REFERENCES
|
Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
|
|
|
LINKS
|
Table of n, a(n) for n=0..24.
|
|
|
FORMULA
|
G.f.: 2x/(3sqrt(1-4x^2)+2x-3); a(0)=1, a(n)=sum{k=0..n, k*binomial(n-1, (n-k)/2)(1+(-1)^(n-k))3^k/(n+k)}, n>0.
Conjecture: 3*n*a(n) -10*n*a(n-1) +12*(3-n)*a(n-2) +40*(n-3)*a(n-3)=0. - R. J. Mathar, Sep 21 2012
|
|
|
CROSSREFS
|
Cf. A100087, A098615.
Sequence in context: A199137 A089978 A052906 * A050181 A089931 A148946
Adjacent sequences: A102895 A102896 A102897 * A102899 A102900 A102901
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Paul Barry, Jan 17 2005
|
|
|
STATUS
|
approved
|
| |
|
|
