

A158499


Expansion of (1+sqrt(14x))/(24x).


1



1, 1, 1, 0, 5, 24, 90, 312, 1053, 3536, 11934, 40664, 140114, 488240, 1719380, 6113200, 21921245, 79200160, 288045110, 1053728920, 3874721030, 14313562480, 53093391980, 197669347600, 738398308850, 2766700765024
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OFFSET

0,5


COMMENTS

Hankel transform is A056594 with g.f. 1/(1+x^2).
Row sums of the Riordan array (sqrt(14x)/(12x),xc(x)^2), c(x) the g.f. of A000108.
The inverse Catalan transform yields A146559.  R. J. Mathar, Mar 20 2009


LINKS

Matthew House, Table of n, a(n) for n = 0..1669


FORMULA

a(n) = Sum_{k=0..n} binomial(2k,k)*A158495(nk).
Conjecture: n*a(n) +6*(1n)*a(n1) +4*(2*n3)*a(n2)=0.  R. J. Mathar, Nov 14 2011
This conjecture has been proven.  Matthew House, Nov 08 2015


MATHEMATICA

CoefficientList[ Series[(1 + Sqrt[1  4x])/(2  4x), {x, 0, 26}], x] (* Robert G. Wilson v, Nov 08 2015 *)


PROG

(PARI) x='x+O('x^33); Vec(((14*x)+sqrt(14*x))/(2*(12*x)*sqrt(14*x))) \\ Altug Alkan, Nov 08 2015


CROSSREFS

Sequence in context: A089095 A220316 A220339 * A074085 A145914 A066316
Adjacent sequences: A158496 A158497 A158498 * A158500 A158501 A158502


KEYWORD

easy,sign


AUTHOR

Paul Barry, Mar 20 2009


EXTENSIONS

Name edited by Matthew House, Nov 08 2015


STATUS

approved



