

A102898


A Catalanrelated transform of 3^n.


7



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
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OFFSET

0,2


COMMENTS

Transform of 1/(13x) 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, SpringerVerlag.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
S. B. Ekhad, M. Yang, Proofs of Linear Recurrences of Coefficients of Certain Algebraic Formal Power Series Conjectured in the OnLine Encyclopedia Of Integer Sequences, (2017)


FORMULA

G.f.: 2*x/(3*sqrt(14*x^2)+2*x3).
a(0)=1, a(n)=sum{k=0..n, k*binomial(n1, (nk)/2)(1+(1)^(nk))3^k/(n+k)}, n>0.
Conjecture: 3*n*a(n) 10*n*a(n1) +12*(3n)*a(n2) +40*(n3)*a(n3)=0.  R. J. Mathar, Sep 21 2012
a(n) ~ 2^(n+2) * 5^(n1) / 3^n.  Vaclav Kotesovec, Feb 01 2014


MATHEMATICA

CoefficientList[Series[2*x/(3*Sqrt[14*x^2]+2*x3), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)


CROSSREFS

Cf. A100087, A098615.
Sequence in context: A199137 A089978 A052906 * A050181 A275690 A089931
Adjacent sequences: A102895 A102896 A102897 * A102899 A102900 A102901


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Jan 17 2005


STATUS

approved



